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This Week's Finds in Mathematical Physics

John Baez

Here is a table of contents for This Week's Finds. You can go to any issue by clicking on it. Unfortunately this table of contents fizzles out at "week239".

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Many of the papers I review are available on the arXiv. If you click on the number of one of these papers, such as arXiv:hep-th/9301028, a magic carpet will carry you to a place where you can read an abstract of the paper, and download it if you like. Click here for more information on how to get papers electronically.

week1

  1. Syzygies among elementary string interactions in 2+1 dimensions, by J. Scott Carter and Masahico Saito, Lett. Math. Phys. 23 (1991), 287-300.

    On formulations and solutions of simplex equations, by J. Scott Carter and Masahico Saito, Intern. J. of Mod. Phys. A., 11 (1996) 4453-4463.

    A diagrammatic theory of knotted surfaces, by J. Scott Carter and Masahico Saito, in Quantum Topology, eds. Randy Baadhio and Louis Kauffman, World Science Publishing, Singapore, 1993, 91-115.

    Reidemeister moves for surface isotopies and their interpretations as moves to movies, by J. Scott Carter and Masahico Saito, Journal of Knot Theory and its Ramifications 2 (1993), 251-284.

  2. Knot theory and quantum gravity in loop space: a primer, by Jorge Pullin, to appear in "Proc. of the Vth Mexican School of Particles and Fields," ed. J. L. Lucio, World Scientific, Singapore, now available as arXiv:hep-th/9301028.

  3. Time, measurement and information loss in quantum cosmology, by Lee Smolin, preprint now available as arXiv:gr-qc/9301016.

week2

  1. Link invariants for intersecting loops, by Daniel Armand Ugon, Rodolfo Gambini, and Pablo Mora, October 1992 preprint, available from Gambini, Instituto de Fi'sica, Facultad de Ciencias, Trista'n Narvaja 1674, Montevideo, Uruguay.

  2. New points of view in knot theory, by Joan Birman, preprint, to appear in the Bulletin of the AMS.

  3. Link polynomials and a graphical calculus, by Louis Kauffman and P. Vogel, Jour. of Knot Theory and its Ramifications, 1 (1992), 59-104.

  4. Categorical physics, by Louis Crane, preprint available as arXiv:hep-th/9301061 in amstex.

    A Categorical construction of 4d topological quantum field theories, by Louis Crane and David Yetter, preprint available as arXiv:hep-th/9301062.

    Hopf Categories and their representations, Louis Crane and Igor Frenkel, draft version.

    Categorification and the construction of topological quantum field theory, Louis Crane and Igor Frenkel, draft version.

  5. The origin of time asymmetry, by S W Hawking, R Laflamme and G W Lyons, preprint available as arXiv:gr-qc/9301017, in tex.

week3

  1. On the Vassiliev Knot Invariants by Dror Bar-Natan, Harvard University ``pre-preprint.''

  2. Mathematical problems of non-perturbative quantum general relativity, by Abhay Ashtekar, lectures delivered at the 1992 Les Houches summer school on Gravitation and Quantization, December 2, 1992, available as Syracuse University physics preprint SU-GP-92/11-2.

week4

  1. Self-organized criticality in Monte Carlo simulated ecosystems, by R. Sole, D. Lopez, M. Ginovart and J. Valls, Phys. Lett. A172 (1992), p. 56.

  2. There are no quantum jumps, nor are there particles!, by H. D. Zeh, Phys. Lett. A173, p. 189.

  3. Braided monoidal 2-categories, 2-vector spaces and Zamolodchikov tetrahedra equations, by M. M. Kapranov and V. A. Voevodsky. Preliminary incomplete version, September 1991.

week5

  1. Vyjayanthi Chari and Alexander Premet, Indecomposable restricted representations of quantum sl2, University of California at Riverside preprint.

  2. David Kazhdan and Iakov Soibelman, Representations of the quantized function algebras, 2-categories and Zamolodchikov tetrahedra equations, Harvard University preprint.

  3. Adrian Ocneanu, A note on simplicial dimension shifting, available as arXiv:hep-th/9302028.

  4. Abhay Ashtekar and Jerzy Lewandowski, Representation theory of analytic holonomy C*-algebras, available as arXiv:gr-qc/9311010.

  5. Abhay Ashtekar and Chris Isham, Representations of the holonomy algebras of gravity and non-Abelian gauge theories, Journal of Classical and Quantum Gravity 9 (1992), 1069-1100. Also available as arXiv:hep-th/9202053.

  6. John Baez, Link invariants, holonomy algebras and functional integration, available as arXiv:hep-th/9301063.

week6

  1. Alexander Vilenkin, Quantum cosmology, talk given at Texas/Pascos 1992 at Berkeley by available as arXiv:gr-qc/9302016

  2. Lee Smolin, Finite, diffeomorphism invariant observables in quantum gravity, available as arXiv:gr-qc/9302011.

  3. Carlo Rovelli, Time in quantum gravity: an hypothesis, Phys. Rev. D43 (1991), 442-456.

  4. Chris J. Isham, Canonical quantum gravity and the problem of time, 125 pages, available as arXiv:gr-qc/9210011.

  5. Lee Smolin, Time, measurement and information loss in quantum cosmology, available as arXiv:gr-qc/9301016.

  6. P. Hajicek, Comment on "Time in quantum gravity - an hypothesis", Phys. Rev. D44 (1991), 1337-1338.

week7

  1. Mathematical problems of non-perturbative quantum general relativity (lectures delivered at the 1992 Les Houches summer school on Gravitation and Quantization), by Abhay Ashtekar, 87 pp, available as arXiv:gr-qc/9302024.

  2. Lectures on Non-perturbative Canonical Gravity, by Abhay Ashtekar, World Scientific Press, 1991. (ISBN 981-02-0573-2 or for paperback, ISBN 981-02-0574-0. This can be ordered by calling World Scientific at 1-800-227-7562.)

  3. We are not stuck with gluing, by David Yetter and Louis Crane, preprint available as arXiv:hep-th/9302118, 2 pages.

  4. The initial value problem in light of Ashtekar's variables, by R. Capovilla, J. Dell and T. Jacobson, preprint available as arXiv:gr-qc/9302020, 15 pages.

  5. Combinatorial expression for universal Vassiliev link invariant, by Sergey Piunikhin, preprint available as arXiv:hep-th/9302084

week8

  1. Map coloring and the vector cross product, by Louis Kauffman, J. Comb. Theory B, 48 (1990) 45.

    Map coloring, 1-deformed spin networks, and Turaev-Viro invariants for 3-manifolds, by Louis Kauffman, Int. Jour. of Mod. Phys. B, 6 (1992) 1765 - 1794.

    An algebraic approach to the planar colouring problem, by Louis Kauffman and H. Saleur, in Comm. Math. Phys. 152 (1993), 565-590.

  2. Knots and physics, by Louis Kauffman, Proc. Symp. Appl. Math. 45 (1992), 131-246.

    Spin networks, topology and discrete physics, by Louis Kauffman, University of Illinois at Chicago preprint.

    Vassiliev invariants and the Jones polynomial, by Louis Kauffman, University of Illinois at Chicago preprint.

    Gauss codes and quantum groups, by Louis Kauffman, University of Illinois at Chicago preprint.

    Fermions and link invariants, by Louis Kauffman and H. Saleur, Yale University preprint YCTP-P21-91, July 5, 1991.

    State models for link polynomials, by Louis Kauffman, L'Enseignement Mathematique, 36 (1990), 1 - 37.

    The Conway polynomial in R^3 and in thickened surfaces: a new determinant formulation, by F. Jaeger, Louis Kauffman and H. Saleur, preprint.

week9

  1. Surgical invariants of four-manifolds, by Boguslaw Broda, preprint available as arXiv:hep-th/9302092.

    Reshetikhin-Turaev and Crane-Kohno-Kontsevich 3-manifold invariants coincide, by Sergey Piunikhin, preprint, 1992. (Piunikhin is at serguei@math.harvard.edu.)

    A link calculus for 4-manifolds, by E. Cesar de Sa, in Topology of Low-Dimensional Manifolds, Proc. Second Sussex Conf., Lecture Notes in Math., vol. 722, Springer, Berlin, 1979, pp. 16-30,

    A note on 4-dimensional handlebodies, by F. Laudenbach and V. Poenaru, Bull. Math. Soc. France 100 (1972), pp. 337-344,

  2. Minisuperspaces: symmetries and quantization, by Abhay Ashtekar, Ranjeet S. Tate and Claes Uggla Syracuse University preprint SU-GP-92/2-5, 14 pages, available as arXiv:gr-qc/9302026

    Minisuperspaces: observables and quantization, Abhay Ashtekar, Ranjeet S. Tate and Claes Uggla Syracuse University preprint SU-GP-92/2-6, 34 pages, available as arXiv:gr-qc/9302027

  3. Unique determination of an inner product by adjointness relations in the algebra of quantum observables, by Alan D. Rendall, Max-Planck-Institut fuer Astrophysik preprint, 10 pages, available as arXiv:gr-qc/9303026.

  4. Thawing the frozen formalism: the difference between observables and what we observe, by Arlen Anderson, preprint available as arXiv:gr-qc/9211028.

  5. Canonical Quantum Gravity and the Problem of Time, Chris J. Isham, 125 pages, preprint available as arXiv:gr-qc/9210011.

  6. The extended loop group: an infinite dimensional manifold associated with the loop space, by Cayetano Di Bartolo, Rodolfo Gambini and Jorge Griego, 42 pages, preprint available as arXiv:gr-qc/9303010.

week10

  1. Beyond Einstein - is space loopy? by Marcia Bartusiak, Discover, April 1993.

  2. Vassiliev invariants contain more information than all knot polynomials, by Sergey Piunikhin, preprint. (Piunikhin is at serguei@math.harvard.edu)

    Turaev-Viro and Kauffman-Lins invariants for 3-manifolds coincide, by Sergey Piunikhin, Journal of Knot Theory and its Ramifications, 1 (1992) 105 - 135.

    Different presentations of 3-manifold invariants arising in rational conformal field theory, by Sergey Piunikhin, preprint.

    Weights of Feynman diagrams, link polynomials and Vassiliev knot invariants, by Sergey Piunikhin, preprint.

    Reshetikhin-Turaev and Crane-Kohno-Kontsevich 3-manifold invariants coincide, by Sergey Piunikhin, preprint.

  3. Bibliography of publications related to classical and quantum gravity in terms of the Ashtekar variables, by Bernd Bruegmann, 14 pages, available as arXiv:gr-qc/9303015.

  4. Surgical invariants of four-manifolds, by Boguslaw Broda, preprint available as arXiv:hep-th/9302092. (Revisited - see "week9")

week11

  1. Unique determination of an inner product by adjointness relations in the algebra of quantum observables, by Alan D. Rendall, 10 pages, now available as arXiv:gr-qc/9303026.

  2. An algebraic approach to the quantization of constrained systems: finite dimensional examples, by Ranjeet S. Tate, Syracuse University physics department PhD dissertation, August 1992, SU-GP-92/8-1. (Tate is now at rstate@cosmic.physics.ucsb.edu, but please don't ask him for copies unless you're pretty serious, because it's big.)

week12

  1. Canonical quantum gravity, by Karel Kuchar, preprint available as arXiv:gr-qc/9304012.

  2. 2-categories and 2-knots, by John Fischer, preprint, last revised Feb. 6 1993. (Fischer is at fischer-john@math.yale.edu)

  3. A new discretization of classical and quantum general relativity, by Mark Miller and Lee Smolin, 22 pages, preprint available as arXiv:gr-qc/9304005.

  4. Higher algebraic structures and quantization, by Dan Freed, preprint, December 18, 1992, available as arXiv:hep-th/9212115; see also week48.

week13

  1. Elliptic Curves by Anthony W. Knapp, Mathematical Notes, Princeton University Press, 1992.

  2. Elliptic Functions by Serge Lang, Springer-Verlag, 2nd edition, 1987.

  3. Elliptic Curves by Dale Husemoeller, Springer-Verlag, 1987.

  4. Closed string field theory, strong homotopy Lie algebras and the operad actions of moduli spaces, by Jim Stasheff, preprint available as arXiv:hep-th/9304061.

  5. A geometrical presentation of the surface mapping class group and surgery, by Sergey Matveev and Michael Polyak, preprint.

  6. Invariants of 3-manifolds and conformal field theories, by Micheal Polyak, preprint.

week14

  1. Skein theory and Turaev-Viro invariants, by Justin Roberts, Pembroke College preprint, April 14, 1993 (Roberts is at J.D.Roberts@pmms.cam.ac.uk)

  2. The basis of the Ponzano-Regge-Turaev-Viro-Ooguri model is the loop representation basis, by Carlo Rovelli, 16 pages, preprint available as arXiv:hep-th/9304164.

  3. Diffeomorphism-invariant generalized measures on the space of connections modulo gauge transformations, by John Baez, to appear in the proceedings of the Conference on Quantum Topology, Manhattan, Kansas, May 8, 1993, also available as state.tex.

  4. Completeness of Wilson loop functionals on the moduli space of SL(2,C) and SU(1,1)-connections, Abhay Ashtekar and Jerzy Lewandowski, 7 pages, preprint available as arXiv:gr-qc/9304044.

  5. An algebraic approach to the quantization of constrained systems: finite dimensional examples, by Ranjeet S. Tate, (Ph.D. Dissertation, Syracuse University), 124 pages, LaTeX (run thrice before printing), available as arXiv:gr-qc/9304043.

  6. SU(2) QCD in the path representation, by Rodolfo Gambini and Leonardo Setaro, 37 pages, preprint available as arXiv:hep-lat/9305001.

week15

  1. Closed string field theory - an introduction, by Barton Zwiebach, preprint available as arXiv:hep-th/9305026 (requires the phyzzx macros to print; these macros are also available from hep-th; see below).

  2. Two-dimensional Yang-Mills theories are string theories, by S.G. Naculich, H.A. Riggs, and H.J. Schnitzer, 14 pages, preprint available as arXiv:hep-th/9305097.

week16

  1. Structure of topological lattice field theories in three dimensions, by Stephen-wei Chung, Masafumi Fukuma and Alfred Shapere, preprint, available as arXiv:hep-th/9305080 (make sure to get the pictures if possible)!

  2. C. Bachas and P. M. S. Petropoulos, Comm. Math. Phys. 152 (1993) 191.

  3. Lattice topological field theory in two-dimensions, by M. Fukuma, S. Hosono and H. Kawai, preprint available as arXiv:hep-th/9212154, now in print in Comm. Math. Phys. 161 (1994) 157-175.

  4. Six ways to quantize (2+1)-dimensional gravity, by Steven Carlip, available as arXiv:gr-qc/9305020.

  5. An illustration of 2+1 gravity loop transform troubles, by Donald Marolf, available as arXiv:gr-qc/9305015.

  6. G. Ponzano and T. Regge: in Bloch, F. (ed.), Spectroscopic and Group Theoretical Methods in Physics, Amsterdam: North-Holland 1968.

  7. 2+1 dimensional gravity as an exactly soluble system, by E. Witten, Nucl. Phys. 311 (1988), 46-78.

  8. State sum invariants of 3-manifolds and quantum 6j-symbols, by V. G. Turaev and O. Y. Viro, Topology 31 (1992), 865.

  9. H. Ooguri, Mod. Phys. Lett. A7 (1992), 2799.

  10. Actions for gravity, with generalizations: a review, by Peter Peldan, 61 pages, available as arXiv:gr-qc/9305011

week17

  1. ``Theoretical Mathematics'': Toward a cultural synthesis of mathematics and theoretical physics, by Arthur Jaffe and Frank Quinn, to appear in the July 1993 Bulletin of the AMS (available by gopher at e-math.ams.com, but don't ask me how).

  2. New Scientific Applications of Geometry and Topology, ed. DeWitt L. Sumner, Proc. Symp. Appl. Math. 45, published by the AMS.

  3. Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds, by Louis Kauffman and Sostenes Lins, to be published by Princeton U. Press.

  4. 12j-symbols and four-dimensional quantum gravity, by M. Carfora, M. Martellini (martellini@milano.infn.it), and A. Marzuoli, Dipartimento di Fisica, Universita di Roma "La Sapienza" preprint.

  5. Selected topics in quantum groups, by Y. S. Soibelman (soibel@math.harvard.edu), Lectures for the European School of Group Theory, Harvard University preprint.

  6. Braids and movies, by J. Scott Carter (carter@mathstat.usouthal.edu) and Masahico Saito, preprint.

  7. Combinatorial Invariants from Four Dimensional Lattice Models: II, by Danny Birmingham and Mark Rakowski, preprint available as arXiv:hep-th/9305022.

  8. A note on the four-dimensional Kirby calculus, by Boguslaw Broda, preprint, 5 pages, preprint available as arXiv:hep-th/9305101.

  9. Solutions to the Wheeler DeWitt constraint of canonical gravity coupled to scalar matter fields, by H.-J. Matschull, preprint available as arXiv:gr-qc/9305025.

week18

  1. Strings, loops, knots, and gauge fields, by John Baez, preprint available as arXiv:hep-th/9309067, 34 pages. Also available in LaTeX as string.tex.

week19

  1. Evaluating the Crane-Yetter Invariant, by Louis Crane, Louis H. Kauffman, David N. Yetter, 4 pages, preprint available as arXiv:hep-th/9309063.

  2. On the Classicality of Broda's SU(2) Invariants of 4-Manifolds, by Louis Crane, Louis H. Kauffman, David N. Yetter, 4 pages, preprint available as arXiv:hep-th/9309102.

  3. Exactly soluble diffeomorphism-invariant theories, by Gary Horowitz, Comm. Math. Phys., 125 (1989) 417-437.

week20

  1. John H. Conway and Neil J. A. Sloane, Sphere Packings, Lattices and Groups, second edition, Grundlehren der mathematischen Wissenschaften 290, Springer-Verlag, 1993.

  2. Igor Frenkel, James Lepowsky, and Arne Meurman, Vertex Operator Algebras and the Monster, Academic Press, New York, 1988.

week21

  1. Knotted surfaces, braid movies, and beyond, by J. Scott Carter and M. Saito, to appear in Knots and Quantum Gravity, ed. John Baez, Oxford U. Press.

  2. How Surfaces Intersect in Space: An Introduction to Topology, by J. Scott Carter, World Scientific Press, Singapore 1993. ISBN 981-02-1050

  3. A Topological Picturebook, by George Francis, Springer-Verlag, 1987.

week22

  1. The Four-Color Problem: Assault and Conquest, by Thomas L. Saaty and Paul C. Kainen, McGraw-Hill, 1977, ISBN 0-07-054382-8.

  2. Map coloring and the vector cross product, by Louis Kauffman, J. Comb. Theory B, 48 (1990) 45.

    Map coloring, 1-deformed spin networks, and Turaev-Viro invariants for 3-manifolds, by Louis Kauffman, Int. Jour. of Mod. Phys. B, 6 (1992) 1765 - 1794.

    An algebraic approach to the planar colouring problem, by Louis Kauffman and H. Saleur, Yale University preprint YCTP-P27-91, November 8, 1991.

  3. Every Planar Map is Four Colorable, by Kenneth Appel and Wolfgang Haken, Contemporary Mathematics (American Mathematical Society), v. 98, 1989.

  4. Applications of negative dimensional tensors, by Roger Penrose, in Combinatorial Mathematics and its Applications, ed. D. J. A. Welsh, Academic Press, 1971.

week23

  1. Topological quantum invariants and the Andrews-Curtis conjecture (Progress report), by Frank Quinn, preprint, Sept. 1993.

  2. Lectures on axiomatic topological quantum field theory, by Frank Quinn, to appear in the proceedings of the Park City Geometry Institute.

  3. On the Andrews-Curtis conjecture and related problems, by Wolfgang Metzler, in Combinatorial Methods in Topology and Algebraic Geometry, Contemporary Mathematics 44, AMS, 1985.

  4. Elements of Homotopy Theory, by George W. Whitehead, Springer-Verlag, Berlin, 1978. ISBN 0-387-90336-4

  5. S. Gelfand and D. Kazhdan, Examples of tensor categories, Invent. Math. 109 (1992) 595-617.

  6. Knots and Quantum Gravity, ed. John Baez, Oxford University Press, Oxford, 1994. ISBN 0-19-853490-6. (This can be ordered by calling 0536 454 534 in the UK, or + 44 536 454 534 outside the UK.)

    The loop formulation of gauge theory and gravity, by Renate Loll

    Representation theory of analytic holonomy C* algebras, by Abhay Ashtekar and Jerzy Lewandowski (currently available as arXiv:gr-qc/9311010)

    The Gauss linking number in quantum gravity, by Rodolfo Gambini and Jorge Pullin (currently available as arXiv:gr-qc/9310025)

    Vassiliev invariants and the loop states in quantum gravity, by Louis H. Kauffman (soon to be on gr-qc)

    Geometric structures and loop variables in (2+1)-Dimensional gravity, by Steven Carlip (currently available as arXiv:gr-qc/9309020)

    From Chern-Simons to WZW via path integrals, by Dana S. Fine

    Topological field theory as the key to quantum gravity, by Louis Crane (currently available as arXiv:hep-th/9308126)

    Strings, loops, knots and gauge gields, by John Baez (currently available as arXiv:hep-th/9309067 and also at string.tex).

    BF Theories and 2-knots, by Paolo Cotta-Ramusino and Maurizio Martellini

    Knotted surfaces, braid movies, and beyond, by J. Scott Carter and Masahico Saito

week24

  1. Prima facie questions in quantum gravity, by Chris Isham, lecture at Bad Honeff, September 1993, preprint available as arXiv:gr-qc/9310031.

  2. Lectures on 2d gauge theories: topological aspects and path integral techniques, by Matthias Blau and George Thompson, 70 pages, preprint available as arXiv:hep-th/9310144.

  3. Semi-classical limits of simplicial quantum gravity, by J. W. Barrett and T. J. Foxon, preprint available as arXiv:gr-qc/9310016.

  4. Wave function of the universe, by J. B. Hartle and S. W. Hawking, Phys. Rev. D28 (1983), 2960.

  5. Generalized measures in gauge theory, by John Baez, available as arXiv:hep-th/9310201. Also available as conn.tex.

week25

  1. Loop Spaces, Characteristic Classes and Geometric Quantization, by Jean-Luc Brylinski, Birkhauser, Boston, 1993. ISBN 0-176-3644-7

  2. Quantization and unitary representations, by Bertram Kostant, in Lectures in Modern Analysis and Applications III, Springer-Verlag Lecture Notes in Mathematics 170 (1970), 87-208.

  3. Vortices in He II, current algebras and quantum knots, by M. Rasetti and T. Regge, Physica 80A (1975) 217-233.

  4. A geometric approach to quantum vortices, by V. Penna and M. Spera, J. Math. Phys. 30 (1989), 2778-2784.

  5. Higher algebraic structures and quantization, by Dan Freed, preprint, December 18, 1992, available as arXiv:hep-th/9212115.

  6. Representation Theory of Analytic Holonomy C* Algebras, by Abhay Ashtekar and Jerzy Lewandowski, to appear in Knots and Quantum Gravity, ed. J. Baez, 42 pages, currently available as arXiv:gr-qc/9311010.

week26

  1. Cosmology, time's arrow, and that old double standard, by Huw Price, 26 pages, available as arXiv:gr-qc/9310022. (Written for Time's Arrows Today Conference, UBC, Vancouver, June 1992; forthcoming in Savitt, S., ed., "Time's Arrows Today," Cambridge University Press, 1994.)

  2. The Physical Basis of the Direction of Time, by H. D. Zeh, Second Edition, Springer-Verlag, 1992. ISBN 3-540-54884-X or 0-387-54884-X

  3. Chromodynamics and gravity as theories on loop space, by R. Loll, 56 pages, 10 figures (postscript, compressed and uuencoded), preprint available as arXiv:hep-th/9309056.

  4. Intersecting braids and intersecting knot theory, by Daniel Armand-Ugon, Rodolfo Gambini and Pablo Mora, Latex 14 pages (6 figures included), available as arXiv:hep-th/9309136.

week27

  1. Conceptual Problems of Quantum Gravity, edited by Abhay Ashtekar and John Stachel, based on the proceedings of the 1988 Osgood Hill Conference, 15-19 May 1988, Birkhaueser, Boston, 1991.

  2. Quantum measurements and the environment-induced transition from quantum to classical, by Wojciech H. Zurek, the volume above.

    Loss of quantum coherence for a damped oscillator, by W. G. Unruh, the volume above.

  3. Is there incompatibility between the ways time is treated in general relativity and in standard quantum mechanics?, by Carlo Rovelli, the volume above.

    The problem of time in canonical quantization of relativistic systems, by Karel V. Kuchar, the volume above.

    Time and prediction in quantum cosmology, by James B. Hartle, the volume above.

    Space and time in the quantum universe, by Lee Smolin, the volume above.

  4. Old problems in the light of new variables, by Abhay Ashtekar, the volume above.

    Loop representation in quantum gravity, by Carlo Rovelli, the volume above.

    Nonperturbative quantum gravity via the loop representation, by Lee Smolin, the volume above.

week28

  1. An Introduction to Teichmueller spaces, by Y. Imayoshi and M. Taniguchi, Springer-Verlag, 1991, ISBN 4-431-70088-9.

  2. An introduction to the moduli space of curves, by Joe Harris, in Mathematical Aspects of String Theory (proceedings of a conference at UC San Diego in 1986), ed. S. T. Yau, World Scientific Press, 1987, ISBN 9971-50-274-7.

  3. The cohomology of the moduli space of curves, by John L. Harer, in Theory of Moduli (lectures given at the 3rd 1985 session of C.I.M.E. at Mondecatini Terme, Italy), ed. E. Sernesi, Springer-Verlag Lecture Notes in Mathematics 1337, 1988, ISBN 0-387-50080-4.

  4. A presentation of the mapping class group of a closed, orientable surface, by A. Hatcher and W. Thurston, Topology 19 (1980), 221-237.

  5. A simple presentation for the mapping class group of an orientable surface, Israel J. Math. 45 (1983), 157-174.

  6. Braids, Links, and Mapping Class Groups, by Joan S. Birman, Annals of Mathematics Studies no. 82, Princeton University Press, 1974.

  7. Universal constructions in Teichmueller theory, by R. C. Penner, Adv. Math. 98 (1993), 143-215.

  8. Classical and quantum conformal field theory, by G. Moore and S. Seiberg, Comm. Math. Phys. 123 (1989) 177-254

  9. 2-d physics and 3-d topology, by Louis Crane, Comm. Math. Phys. 135 (1991) 615-640.

week29

  1. On algebras and triangle relations, by Ruth J. Lawrence, to appear in Proc. Top. & Geom. Methods in Field Theory (1992), eds. J. Mickelsson and O. Pekonen, World Scientific, Singapore.

    A presentation for Manin and Schechtman's higher braid groups, by R. J. Lawrence, available as MSRI preprint 04129-91.

    Triangulations, categories and extended topological field theories, by R. J. Lawrence, in Quantum Topology, eds L. Kauffman and R. Baadhio, World Scientific, Singapore, 1993.

    Algebras and triangle relations, by R. J. Lawrence, Harvard U. preprint.

  2. Coherence for tricategories, by R. Gordon, A. J. Power, and R. Street, preprint, 81 pages.

  3. Formal Category Theory: Adjointness for 2-categories, by John W. Gray, Lecture Notes in Mathematics 391, Springer-Verlag, New York, 1974. ISBN 3-540-06830-9.

    Coherence for the tensor product of 2-categories, and braid groups, in Algebras, Topology, and Category Theory, eds. A. Heller and M. Tierney, Academic Press, New York, 1976, pp. 63-76.

  4. On pentagon and tetrahedron equations, by J. M. Maillet, preprint available as arXiv:hep-th/9312037.

  5. Homologically twisted invariants related to (2+1)- and (3+1)-dimensional state-sum topological quantum field theories, by David N. Yetter, preprint, 6 pages, available as arXiv:hep-th/9311082.

week30

  1. QED and the Men Who Made It: Dyson, Feynman, Schwinger and Tomonaga, by Silvan S. Schweber, Princeton Series in Physics, Princeton U. Press, 784 pages, available May 1994. Paperback: ISBN 0-691-03327-3 ($39.50).

  2. The Music of the Heavens: Kepler's Harmonic Astronomy, by Bruce Stephenson, Princeton U. Press, 296 pages, available July 1994. Cloth: ISBN 0-691-03439-7 ($39.50).

    Kepler's Physical Astronomy, by Bruce Stephenson, Princeton U. Press, 218 pages, paperback available June 1994. ISBN 0-691-03652-7 ($14.95).

  3. Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds, by Louis Kauffman and Sostenes Lins, Annals of Mathematics Studies No. 133, Princeton U. Press, 304 pages, available July 1994. Paperback: ISBN 0-691-03640-3 ($22.50).

  4. The physical hamiltonian in quantum gravity, by C. Rovelli and L. Smolin, 11 pages, preprint available as arXiv:gr-qc/9308002.

    Fermions in quantum gravity, by H. A. Morales-Tecotl and C. Rovelli, 37 pages, preprint available as arXiv:gr-qc/9401011.

  5. Extended loops: a new arena for nonperturbative quantum gravity, by C. Di Bartolo, R. Gambini, J. Griego and J. Pullin, 12 pages, preprint available in Revtex form as arXiv:gr-qc/9312029.

  6. Ashtekar variables in classical general relativity, by Domenico Giulini, 43 pages, preprint available as arXiv:gr-qc/9312032.

week31

  1. Possible implications of the quantum theory of gravity, by Louis Crane, 5 pages, preprint available as arXiv:hep-th/9402104.

  2. S. W. Hawking, Phys. Rev. D13, 191 (1976).

  3. Do black holes destroy information? by J. Preskill, Caltech report CALT-68-1819, available as arXiv:hep-th/9209058, Sept. 1992.

  4. Black hole information, by Don Page, review lecture to be published in Proceedings of the 5th Canadian Conference on General Relativity and Relativistic Astrophysics, University of Waterloo, 13--15 May, 1993}, edited by R. B. Mann and R. G. McLenaghan (World Scientific, Singapore, 1994) now available as arXiv:hep-th/9305040.

  5. Some speculations about black hole entropy in string theory, Leonard Susskind, 11 pages, preprint available as arXiv:hep-th/9309145.

    Black hole entropy in canonical quantum gravity and superstring theory, by L. Susskind and J. Uglum, 29 pages, available as arXiv:hep-th/9401070.

  6. Black hole evaporation without information loss, by C.R. Stephens, G. 't Hooft and B. F. Whiting, 35 pages, 3 figures in postscript, preprint available as arXiv:gr-qc/9310006.

  7. Complementarity in wormhole chromodynamics, by Hoi-Kwong Lo, Kai-Ming Lee, and John Preskill, 12 pages and 2 figures, phyzzx macros required, available as arXiv:hep-th/9308044.

  8. "No hair" theorems -- folklore, conjectures, results, by Piotr T. Chrusciel, Garching preprint MPA 792, 30 pages available as arXiv:gr-qc/9402032.

  9. On uniqueness in the large of solutions of Einstein's equations ("Strong cosmic censorship"), by Piotr T. Chrusciel, in Mathematical Aspects of Classical Field Theory, Contemp. Math. 132, eds. Gotay, Marsden and Moncrief, AMMS, Rhode Island, 1992, pp. 235-274.

week32

  1. On quantum mechanics, by Carlo Rovelli, uuencoded PostScript file, 42 pages available as arXiv:hep-th/9403015.

  2. Adjointness relations as a criterion for choosing an inner product, by Alan Rendall, arXiv:gr-qc/9403001.

  3. Gromov-Witten classes, quantum cohomology, and enumerative geometry, by M. Kontsevich, Yu. Manin, arXiv:hep-th/9402147.

week33

  1. Gauge Fields, Knots and Gravity, by John Baez and Javier de Muniain, World Scientific Press. (ISBN 981-02-1729-3, or ISBN 981-02-2034-0 for paperback. This can be ordered by calling World Scientific at 1-800-227-7562.)

  2. Quantum Theory: Concepts and Methods, by Asher Peres, Kluwer Academic Publishers, 1994, ISBN 0-7923-2549-4.

  3. Loop representations, by Bernd Bruegmann, Max Planck Institute preprint, available as gr-qc 9312001.

  4. The fate of black hole singularities and the parameters of the standard models of particle physics and cosmology, by Lee Smolin, preprint available as arXiv:gr-qc/9404011.

week34

  1. Algorithms for quantum computation: discrete log and factoring, extended abstract by Peter Shor.

  2. Simulating physics with computers, by Richard Feynman, International Journal of Theoretical Physics, Vol. 21, nos. 6/7, pp. 467--488 (1982).

  3. Quantum mechanical Hamiltonian models of Turing machines, by P. Benioff J. Stat. Phys., Vol. 29, pp. 515--546 (1982).

    Quantum theory, the Church--Turing principle and the universal quantum computer, by D. Deutsch, Proc. R. Soc. Lond., Vol. A400, pp. 96--117 (1985).

    Quantum computational networks, by D. Deutsch, Proc. R. Soc. Lond., Vol. A425, pp. 73--90 (1989).

    Rapid solution of problems by quantum computation, by D. Deutsch and R. Jozsa, Proc. R. Soc. Lond., Vol. A439, pp. 553--558 (1992).

    Quantum complexity theory, E. Bernstein and U. Vazirani, Proc. 25th ACM Symp. on Theory of Computation, pp. 11--20 (1993).

    The quantum challenge to structural complexity theory, A. Berthiaume and G. Brassard, Proc. 7th IEEE Conference on Structure in Complexity Theory (1992).

    Quantum circuit complexity, by A. Yao, Proc. 34th IEEE Symp. on Foundations of Computer Science, 1993.

  4. The Chern-Simons invariant as the natural time variable for classical and quantum cosmology, by Lee Smolin and Chopin Soo, 16 pages, preprint available as arXiv:gr-qc/9405015.

  5. Symplectic geometry, a series of lectures by Mikhail Gromov, compiled by Richard Brown, edited by Robert Miner (lena@math.umd.edu).

week35

  1. Pursuing stacks (A la poursuite des champs), 1983 letter from Alexandre Grothendieck to Daniel Quillen, 593 pages, apparently available only from someone who wants to copy 593 pages for you - i.e., not me!

  2. J. Benabou, Introduction to bicategories, Lect. Notes in Math., vol. 47, Berlin, Springer-Verlag, 1968, pp. 1-71.

  3. Selected bibliography on higher-dimensional algebra.

week36

  1. Three-dimensional BF theories and the Alexander-Conway invariant of knots, by A. S. Cattaneo, P. Cotta-Ramusino, and M. Martellini; 32 pages (figures available upon request), available as arXiv:hep-th/9407070.

  2. B^F theory and flat spacetimes, by Henri Waelbroeck, 21 pages, preprint available as arXiv:gr-qc/9311033.

  3. A Hamiltonian formulation of topological gravity, by Henri Waelbrock and J. A. Zapata, 15 pages, preprint available as arXiv:gr-qc/9311035.

  4. Topological Yang-Mills symmetry, by L. Baulieu and I. M. Singer, Nucl. Phys. (Proc. Suppl.) B5 (1988) 12-19.

  5. On quantum gauge theories in two dimensions, by Edward Witten, Comm. Math. Phys. 141 (1991) 153-209.

  6. Topological gauge theories of antisymmetric tensor fields, by M. Blau and G. Thompson, Ann. Phys. 205 (1991) 130-172.

week37

  1. L. Lindblom, Superfluid hydrodynamics and the stability of rotating neutron stars, talk at MG7 meeting, Monday July 5, Stanford University.

  2. Abhay Ashtekar, Mathematical developments in quantum general relativity, a sampler, talk at MG7 meeting, Tuesday July 6, Stanford University. Available as arXiv:gr-qc/9411055.

week38

  1. Topological quantum field theories from generalized 6j-symbols, B. Durhuus, H. P. Jakobsen and R. Nest, Reviews in Math. Physics 5 (1993), 1-67.

  2. Spin networks, Turaev-Viro theory and the loop representation, by Timothy J. Foxon, preprint available as arXiv:gr-qc/9408013.

  3. Involutory Hopf algebras and three-manifold invariants, by Greg Kuperberg, Internat. Jour. Math 2 (1991), 41-66.

    A definition of #(M,H) in the non-involutory case, by Greg Kuperberg, unpublished.

  4. Spherical categories, by John W. Barrett and Bruce W. Westbury, preprint available as arXiv:hep-th/9310164.

    Invariants of piecewise-linear 3-manifolds, by John W. Barrett and Bruce W. Westbury, Trans. Amer. Math. Soc. 348 (1996), 3997-4022, preprint available as arXiv:hep-th/9311155.

    The equality of 3-manifold invariants, by John W. Barrett and Bruce W. Westbury, preprint available as arXiv:hep-th/9406019.

  5. Invariants of 3-Manifolds derived from finite dimensional Hopf algebras, by Louis H. Kauffman and David E. Radford, 33 pages, preprint available as arXiv:hep-th/9406065.

  6. Four dimensional topological quantum field theory, Hopf categories, and the canonical bases, by Louis Crane and Igor Frenkel, available as arXiv:hep-th/9405183.

  7. A manifestly gauge-invariant approach to quantum theories of gauge fields, by A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourao, T. Thiemann, contribution to the Cambridge meeting proceedings, 27 pages, preprint available as arXiv:hep-th/9408108.

    Topological measure and graph-differential geometry on the quotient space of connections, Jerzy Lewandowski, 3 pp., Proceedings of ``Journees Relativistes 1993'', 3 pages available as arXiv:gr-qc/9406025.

    Integration on the space of connections modulo gauge transformations, Abhay Ashtekar, Donald Marolf, Jose Mourao, 18 pages, preprint available as arXiv:gr-qc/9403042.

    New loop representations for 2+1 gravity, by A. Ashtekar and R. Loll, 28 pages, preprint available as arXiv:gr-qc/9405031.

    Independent loop invariants for 2+1 gravity, by R. Loll, 2 figures, arXiv:gr-qc/9408007.

    Generalized coordinates on the phase space of Yang-Mills theory, by R. Loll, J.M. Mour\~ao and J.N. Tavares, 11 pages, preprint available as arXiv:gr-qc/9404060.

    The extended loop representation of quantum gravity, C. Di Bartolo, R. Gambini and J. Griego, 27 pages available as arXiv:gr-qc/9406039.

    The constraint algebra of quantum gravity in the loop representation, by Rodolfo Gambini, Alcides Garat and Jorge Pullin, 18 pages in Revtex, available as arXiv:gr-qc/9404059.

week39

  1. Noncommutative Geometry, by Alain Connes, Academic Press, 640 pp., $59.95 (tentative), ISBN 0-12-185860-X. (Orders can be placed in the US by calling 1-800-321-5068.)

  2. 2d Yang-Mills theory and topological field theory, by Gregory Moore, available as arXiv:hep-th/9409044.

  3. Strings and two-dimensional QCD for finite N, by J. Baez and W. Taylor, 19 pages available as arXiv:hep-th/9401041, or in LaTeX as string2.tex. To appear in Nuc. Phys. B.

  4. The symplectic nature of fundamental groups of surfaces, by W. Goldman, Adv. Math. 54 (1984), 200-225.

    Invariant functions on Lie groups and Hamiltonian flows of surface group representations, by W. Goldman, Invent. Math. 83 (1986), 263-302.

    Topological components of spaces of representations, by W. Goldman, Invent. Math. 93 (1988), 557-607.

  5. "The Geometry and Physics of Knots," by Michael Atiyah, Cambridge U. Press, Cambridge, 1990.

  6. Group cohomology construction of the cohomology of moduli spaces of flat connections on 2-manifolds, by Lisa C. Jeffrey, preprint available from Princeton U. Mathematics Department.

week40

  1. Linear Logic, by Jean-Yves Girard, Theoretical Computer Science 50 (1987) pp. 1-102.

  2. Linear logic for generalized quantum mechanics, by Vaughan Pratt, available in LaTeX format (compressed) by anonymous ftp from boole.stanford.edu, as the file pub/ql.tex.Z

  3. Hopf algebras and linear logic, by Richard Blute, to appear in Mathematical Structures in Computer Science.

  4. Linear logic, *-autonomous categories and cofree coalgebras, by R. A. G. Seely, in Categories in Computer Science and Logic, Contemp. Math. 92 (1989).

  5. Quantales and (noncommutative) linear logic, by D. Yetter, Journal of Symbolic Logic 55 (1990), 41-64.

week41

  1. The Statistical Mechanics of the (2+1)-Dimensional Black Hole, by Steve Carlip, 12 pages available as arXiv:gr-qc/9409052.

  2. Angular momentum; an approach to combinatorial space time, by Roger Penrose, in "Quantum Theory and Beyond," ed. T. Bastin, Cambridge University Press, Cambridge, 1971.

  3. Conformal field theory, spin geometry, and quantum gravity, by Louis Crane, Phys. Lett. B259 (1991), 243-248.

  4. Von Neumann algebra automorphisms and time-thermodynamics relation in general covariant quantum theories, by A. Connes and C. Rovelli, 25 pages in LaTex format available as arXiv:gr-qc/9406019.

  5. The affine symmetry of self-dual gravity, by Viqar Husain, 17 pages, preprint available as arXiv:hep-th/9410072.

  6. Knots and quantum gravity: progress and prospects, John Baez, 22 pages, preprint available as arXiv:gr-qc/9410018.

  7. "Matters of Gravity", a newsletter for the gravity community, Number 4, edited by Jorge Pullin, 24 pages, preprint available as arXiv:gr-qc/9409004, or from WWW by http://www.phys.lsu.edu//mog/

week42

  1. QCD and the string model, by Y. Nambu, Phys. Lett. B80 (1979) 372-376.

    Gauge fields as rings of glue, A. Polyakov, Nucl. Phys. B164 (1979) 171-188.

    The quantum dual string wave functional in Yang-Mills theories, by J. Gervais and A. Neveu, Phys. Lett. B80 (1979), 255-258.

    The interaction among dual strings as a manifestation of the gauge group, by F. Gliozzi and M. Virasoro, Nucl. Phys. B164 (1980), 141-151.

    Loop-space representation and the large-N behavior of the one-plaquette Kogut-Susskind Hamiltonian, A. Jevicki, Phys. Rev. D22 (1980), 467-471.

    Quantum chromodynamics as dynamics of loops, by Y. Makeenko and A. Migdal, Nucl. Phys. B188 (1981) 269-316.

    Loop dynamics: asymptotic freedom and quark confinement, by Y. Makeenko and A. Migdal, Sov. J. Nucl. Phys. 33 (1981) 882-893.

  2. Conformal field theory, by Krzysztof Gawedzki, Seminaire Bourbaki, Asterisque 177-178 (1989), pp. 95-126.

  3. Introduction to Superstrings, by Michio Kaku, New York, Springer-Verlag, 1988.

    String Fields, Conformal Fields, and Topology, by Michio Kaku, New York, Springer-Verlag, 1991.

  4. Quantum background independence of closed string field theory, by Ashoke Sen and Barton Zwiebach, 60 pages, phyzzx.tex, MIT-CTP-2244, available as arXiv:hep-th/9311009.

    Background independent algebraic structures in closed string field theory, by Ashoke Sen and Barton Zwiebach, phyzzx.tex, MIT-CTP-2346, available as arXiv:hep-th/9408053.

  5. Loop representation for quantum general relativity, by C. Rovelli and L. Smolin, Nucl. Phys. B331 (1990), 80-152.

  6. Gauge dynamics in the C-representation, by R. Gambini and A. Trias, Nucl. Phys. B278 (1986) 436-448.

  7. Infinite Loop Spaces, by J. F. Adams, Princeton U. Press, Princeton, NJ, 1978.

  8. Closed string field theory, strong homotopy Lie algebras and the operad actions of moduli spaces, by Jim Stasheff, available as arXiv:hep-th/9304061.

  9. Loop groups, by Andrew Pressley and Graeme Segal, Oxford University Press, Oxford, 1986.

  10. A reformulation of the Ponzano-Regge quantum gravity model in terms of surfaces, Junichi Iwasaki, University of Pittsburgh, 11 pages, preprint available as arXiv:gr-qc/9410010.

  11. Lattice QCD as a theory of interacting surfaces, by B. Rusakov, TAUP-2204-94, 12 pages, preprint available as arXiv:hep-th/9410004.

    U(N) Gauge Theory and lattice strings, by Ivan K. Kostov, 26 pages, 8 figures not included, available by mail upon request, T93-079 (talk at the Workshop on string theory, gauge theory and quantum gravity, 28-29 April 1993, Trieste, Italy), available as arXiv:hep-th/9308158.

  12. Chern-Simons-Witten theory as a topological Fermi liquid, by Michael R. Douglas, Rutgers University preprint RU-94-29, available as arXiv:hep-th/9403119.

week43

  1. Quantum theory of gravity, I-III by Bryce S. DeWitt, Phys. Rev. 160 (1967), 1113-1148, 162 (1967) 1195-1239, 1239-1256.

  2. Coherent state transforms for spaces of connections, by Abhay Ashtekar, Jerzy Lewandowski, Donald Marolf, Jose Mourao and Thomas Thiemann, 38 pages, preprint available as arXiv:gr-qc/9412014.

    Quantum geometrodynamics, by A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourao and T. Thiemann, in progress, to appear on gr/qc.

  3. The Hamiltonian constraint in quantum gravity, M. Blencowe, Nucl. Phys. B341 (1990), 213-251.

    On the constraints of quantum gravity in the loop representation, Bernd Bruegmann and Jorge Pullin, Nucl. Phys. B390 (1993), 399-438.

    On the constraints of quantum general relativity in the loop representation, Bernd Bruegmann, Ph.D. Thesis, Syracuse University (May 1993).

  4. State-sum invariants of manifolds, I, by Louis Crane, Louis H. Kauffman, and David N. Yetter, 46 pages, LaTeX (Sun release 4.1) source code produces many error messages, but a correct dvi-file, available as arXiv:hep-th/9409167.

  5. Spin networks in gauge theory, by John Baez, 19 pages, preprint available as arXiv:gr-qc/9411007 or in LaTeX at spin.tex.

  6. Discreteness of area and volume in quantum gravity, by Carlo Rovelli and Lee Smolin, 36 pages, preprint available as arXiv:gr-qc/9411005.

week44

  1. "The Geometry of Four-Manifolds," by Simon K. Donaldson and P. B. Kronheimer, Oxford University Press, Oxford, 1990.

    Polynomial invariants for smooth four-manifolds, by S. K. Donaldson, Topology 29 (1990), 257-315.

    "Instantons and Four-Manifolds," by Daniel S. Freed and Karen K. Uhlenbeck, Springer-Verlag, New York (1984).

    "Differential Topology and Quantum Field Theory," by Charles Nash, Academic Press, London, 1991.

  2. Geometry of four dimensional manifolds, by Simon K. Donaldson, videocassette (ca. 60 min.), color, 1/2 in., American Mathematical Society, Providence RI, 1988.

  3. "Spin Geometry," by H. Blaine Lawson, Jr. and Marie-Louise Michelson, Princeton U. Press, Princeton, 1989.

week45

  1. The genus of embedded surfaces in the projective plane, by P. B. Kronheimer and T. S. Mrowka, 10 pages.

  2. Monopoles and four-manifolds, by Edward Witten, in preparation.

    Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory, by Nathan Seiberg and Edward Witten, 45 pages, available as arXiv:hep-th/9407087.

    Monopoles, duality and chiral symmetry breaking in N=2 supersymmetric QCD, by Nathan Seiberg and Edward Witten, 89 pages, available as arXiv:hep-th/9408099.

week46

  1. The speed of write, by Gary Stix, Scientific American, Dec. 1994, 106-111.

    Goodbye, Gutenberg, by Jacques Leslie, WiReD 2.10, Oct. 1994, available via WWW as http://www.hotwired.com/Lib/Wired/2.10/departments /electrosphere/ejournals.html

  2. Monopoles and four-manifolds, by Edward Witten, preprint available as arXiv:hep-th/9411102.

    The genus of embedded surfaces in the projective plane, by P. B. Kronheimer and T. S. Mrowka, preprint number #19941128001, available from the AMS preprint server under subject 57 in the Mathematical Reviews Subject Classification Scheme.

  3. Spin networks in quantum gravity, by Carlo Rovelli and Lee Smolin, to appear.

  4. Recent mathematical developments in quantum general relativity, by Abhay Ashtekar, 14 pages in TeX format available as arXiv:gr-qc/9411055 (discussed in "week37").

    Coherent state transforms for spaces of connections, by Abhay Ashtekar, Jerzy Lewandowski, Donald Marolf, Jose Mourao and Thomas Thiemann, Jour. Funct. Analysis 135 (1996), 519-551, preprint available as arXiv:gr-qc/9412014 (discussed in "week43")

  5. Differential geometry on the space of connections via graphs and projective limits, by Abhay Ashtekar and Jerzy Lewandowski, Jour. Geom. and Phys. 17 (1995), 191-230, preprint available as arXiv:hep-th/9412073.

  6. Edge states in gravity and black hole physics, by A. P. Balachandran, L. Chandar, Arshad Momen, 22 pages in RevTeX format, available as arXiv:gr-qc/9412019.

  7. Quantum gravity and the algebra of tangles, by John Baez, Jour. Class. Quantum Grav. 10 (1993), 673 - 694.

  8. On algebraic structures implicit in topological quantum field theories, by Louis Crane and David Yetter, 13 pages available as arXiv:hep-th/9412025, figures available by request.

  9. On the definition of 2-category of 2-knots, by V. M. Kharlamov and V. G. Turaev, preprint.

  10. Non-involutory Hopf algebras and 3-manifold invariants, by Greg Kuperberg, preprint #19941128002, available from the AMS preprint server under subject 57 or 16 in the Mathematical Reviews Subject Classification Scheme.

  11. If Hamilton had prevailed: quaternions in physics, by J. Lambek, McGill University preprint, Nov. 1994.

  12. The life and times of Emmy Noether; contributions of E. Noether to particle physics, by Nina Byers, 32 pages in RevTeX format, available as arXiv:hep-th/9411110.

    Reminiscences about many pitfalls and some successes of QFT within the last three decades, by B. Schroer, 52 pages, 'shar'-shell-archiv, consisting of 5 files, available as arXiv:hep-th/9410085.

    My encounters - as a physicist - with mathematics, R. Jackiw, 13 pages, preprint available as arXiv:hep-th/9410151.

  13. Speedup in quantum computation is associated with attenuation of processing probability, by Karl Svozil, available as arXiv:hep-th/9412046.

week47

    A description of some new electronic venues for math and physics papers.

week48

  1. Quantum groups from path integrals, by Daniel Freed, preprint, 41 pages in AMSTeX 2.1 format available as arXiv:q-alg/9501025.

  2. Higher algebraic structures and quantization, by Daniel Freed, Comm. Math. Phys. 159 (1994), 343-398; preprint available as arXiv:hep-th/9212115.

  3. Chern-Simons theory with finite gauge group, by Daniel Freed and Frank Quinn, Comm. Math. Phys. 156 (1993), 435-472.

  4. Poisson structures on moduli of flat connections on Riemann surfaces and r-matrices, V. V. Fock and A. A. Rosly, preprint ITEP 72-92, June 1992, Moscow.

  5. Combinatorial quantization of the Hamiltonian Chern-Simons theory, I & II, by Yu. Alekseev, H. Grosse, and V. Schomerus, arXiv:hep-th/9403066 and arXiv:hep-th/9408097.

  6. Geometric quantization of Chern-Simons gauge theory, S. Axelrod, S. Della Pietra and E. Witten, Jour. Diff. Geom. 33 (1991), 787-902.

  7. Metaplectic quantization of the moduli space of flat and parabolic bundles (after Peter Scheinhost), in Public. I. R. M. A. Strasbourg, 45 (1993), 43-70.

week49

  1. Saunders Mac Lane, Categories for the Working Mathematician, Springer, Berlin, 1988.

  2. John Baez and James Dolan, Higher-dimensional algebra and topological quantum field theory, Jour. Math. Phys. 36 (1995), 6073-6105. Also available at arXiv:q-alg/9503002.

  3. Christian Kassel and Vladimir Turaev, Double construction for monoidal categories, Publication de l'Institute de Recherche Mathematique Avancee, 1992.

  4. Martin Neuchl and Peter Schauenburg, Reconstruction in braided categories and a notion of commutative bialgebra, Mathematisches Institut, Theresienstr. 39, 80333 Muenchen, Feb. 20, 1995.

  5. Peter Schauenburg, Tannaka duality for arbitrary Hopf algebras, Algebra-Berichte 66 (1992).

week50

  1. Supersymmetric Yang-Mills theory on a four-manifold, by Edward Witten, Jour. Math. Phys. 35 (1994), 5101-5135.

  2. Four-dimensional topological quantum field theory, Hopf categories, and the canonical bases, by Louis Crane and Igor Frenkel, Jour. Math. Phys. 35 (1994), 5136-5154.

  3. On the self-linking of knots, by Raoul Bott and Clifford Taubes, Jour. Math. Phys. 35 (1994), 5247-5287.

  4. An explicit description of the symplectic struture of moduli spaces of flat connections, by Christopher King and Ambar Sengupta, Jour. Math. Phys. 35 (1994), 5338-5353.

    The semiclassical limit of the two-dimensional quantum Yang-Mills model, same authors, Jour. Math. Phys. 35 (1994), 5354-5363.

  5. Topological interpretations of quantum Hall conductance, by D. J. Thouless, Jour. Math. Phys. 35 (1994), 5362-5372.

  6. The noncommutative geometry of the quantum Hall effect, by J. Bellisard, A. van Elst, and H. Schulz-Baldes, Jour. Math. Phys. 35 (1994), 5373-5451.

  7. Topology change in (2+1)-dimensional gravity, by Steve Carlip and R. Cosgrove, Jour. Math. Phys. 35 (1994), 5477-5493.

week51

  1. Topological quantum field theory, by Edward Witten, Comm. Math. Phys. 117 (1988) 353.

  2. Quantum field theory and the Jones polynomial, by Edward Witten, Comm. Math. Phys. 121 (1989) 351.

  3. N = 2 topological gauge theory, the Euler characteristic of moduli spaces, and the Casson invariant, by Matthias Blau and George Thompson, Comm. Math. Phys. 152 (1993), 41-71.

  4. Knots and Physics, by Louis Kauffman, World Scientific Press, Singapore, 1991.

week52

  1. Permutation City, by Greg Egan, published in Britain by Millenium (should be available in the U.S. by autumn).

  2. Alberto Cattaneo, Teorie topologiche di tipo BF ed invarianti dei nodi, doctoral thesis, department of physics, University of Milan.

    Alberto Cattaneo, Paolo Cotta-Ramusino, Juerg Froehlich, and Maurizio Martellini, Topological BF theories in 3 and 4 dimensions, preprint available as arXiv:hep-th/9505027.

week53

  1. Ronald Brown, Out of line, Royal Institution Proceedings 64, 207-243.

  2. A. J. Power, Why tricategories?, preprint available as ECS-LFCS-94-289 from Laboratory for Foundations of Computer Science, University of Edinburgh. Also available at http://www.ima.umn.edu/talks/workshops/SP6.7-18.04/power/power.pdf

  3. P. Gabriel and F. Ulmer, Lokal praesentierbare Kategorien, in Springer Lecture Notes in Math 221 (1971).

    G. Kelly, Structures defined by finite limits in the enriched context I, Cahiers de Top. et. Geom. Diff. 23 (1982), 3-41.

    Michael Makkai and Robert Pare, Accessible categories: the foundations of categorical model theory, in Contemp. Math. 104 (1989).

week54

  1. Timothy Porter, Abstract homotopy theory: the interaction of category theory and homotopy theory, lectures from the school on "Categories and Topology", Department of Mathematics, Universita di Genova, report #199, March 1992.

  2. L. Loday, Spaces with finitely many non-trivial homotopy groups, Jour. Pure Appl. Algebra 24 (1982), 179-202.

  3. Timothy Porter, Interpretations of Yetter's notion of G-coloring: simplicial fibre bundles and non-abelian cohomology, available at http://citeseer.ist.psu.edu/100965.html

  4. David N. Yetter, Topological quantum field theories associated to finite groups and crossed G-sets, Journal of Knot Theory and its Ramifications 1 (1992), 1-20.

    TQFTs from homotopy 2-types, Journal of Knot Theory and its Ramifications 2 (1993), 113-123.

  5. Justin Roberts, Skein theory and Turaev-Viro invariants, preprint. (Justin Roberts can be reached via email at J.D.Roberts@pmms.cam.ac.uk)

    Refined state-sum invariants of 3- and 4-manifolds, preprint.

    Skeins and mapping class groups, Math. Proc. Camb. Phil. Soc. 115 (1994), 53-77.

    G. Masbaum and Justin Roberts, On central extensions of mapping class groups, Mathematica Gottingensis, Schriftenreihe des Sonderforschungsbereichs Geometrie und Analysis, Heft 42 (1993).

  6. Lawrence Breen, On the Classification of 2-Gerbes and 2-Stacks, Asterisque 225, 1994.

week55

  1. Gary Au, The quest for quantum gravity, available as gr/qc-9506001.

  2. Renate Loll, Nonperturbative solutions for lattice quantum gravity, preprint available as arXiv:gr-qc/9502006.

  3. C. Rovelli and L. Smolin, Spin networks in quantum gravity, preprint available as gr/qc-9505006.

  4. J. Baez, Spin networks in nonperturbative quantum gravity, preprint available as arXiv:gr-qc/9504036, or at net.tex.

  5. Abhay Ashtekar, Jerzy Lewandowski, Don Marolf, Jose Mourao, and Thomas Thiemann, Quantization of diffeomorphism invariant theories of connections with local degrees of freedom, to appear in the November 1995 Jour. Math. Phys. special issue on diffeomorphism-invariant field theory, preprint available as arXiv:gr-qc/9504018.

  6. Steve Sawin, Path integration in two-dimensional topological quantum field theory, to appear in the November 1995 Jour. Math. Phys. issue on diffeomorphism-invariant field theory, preprint available as gr/qc-9505040.

week56

  1. Lee Smolin, Linking topological quantum field theory and nonperturbative quantum gravity, available as arXiv:gr-qc/9505028.

  2. H. Kodama, Holomorphic wavefunction of the universe, Phys. Rev. D42 (1990), 2548-2565.

  3. Louis Crane: Clock and category: is quantum gravity algebraic?, to appear in the November 1995 special issue of Jour. Math. Phys. on diffeomorphism-invariant physics, preprint available as arXiv:gr-qc/9504038.

  4. John Baez, Quantum gravity and the algebra of tangles, Jour. Class. Quant. Grav. 10 (1993), 673-694, also available (without the all-important pictures!) as tang.tex.

week57

  1. Lee Smolin, Linking topological quantum field theory and nonperturbative quantum gravity, available as arXiv:gr-qc/9505028.

  2. G 't Hooft, Dimensional reduction in quantum gravity, preprint available as arXiv:gr-qc/9310006.

  3. L. Susskind, The world as a hologram, to appear in the November 1995 special issue of Jour. Math. Phys. on diffeomorphism-invariant physics, preprint available as arXiv:hep-th/9409089.

    L. Susskind, Strings, black holes and Lorentz contractions, preprint available as arXiv:hep-th/9308139.

week58

  1. John Barrett, Quantum gravity as topological quantum field theory, to appear in the November 1995 special issue of Jour. Math. Physics, also available as arXiv:gr-qc/9506070.

  2. M. Kapranov and V. Voevodsky, 2-Categories and Zamolodchikov tetrahedra equations, in Proc. Symp. Pure Math. 56, Part 2 (1994), AMS, Providence, pp. 177-260.

  3. David Yetter, Categorical linear algebra: a setting for questions from physics and low-dimensional topology, Kansas U. preprint, available as http://math.ucr.edu/home/baez/yetter.pdf and http://math.ucr.edu/home/baez/yetter.ps

  4. Eugenia Cesar de Sa, Automorphisms of 3-manifolds and representations of 4-manifolds, Ph.D. thesis, University of Warwick, 1977.

  5. John Baez, 4-dimensional BF theory as a topological quantum field theory, available as arXiv:q-alg/9507006.

  6. Timothy Porter, TQFTs from homotopy n-types, University of Wales, available at http://www.bangor.ac.uk/~mas013/preprint.html

  7. David Yetter, TQFTs from homotopy 2-types, Journal of Knot Theory and its Ramifications 2 (1993), 113-123.

week59

  1. Geoffrey M. Dixon, Division Algebras: Octonions, Quaternions, Complex Numbers and the Algebraic Design of Physics, Kluwer Press, ISBN 0-7923-2880-6.

  2. William Fulton and Joe Harris, Representation Theory --- a First Course, Springer Verlag, Berlin, 1991.

  3. Geoffrey Dixon, Octonion X-product orbits, preprint available as arXiv:hep-th/9410202.

    Octonion X-product and E8 lattices, preprint available as arXiv:hep-th/9411063.

    Octonions: E8 lattice to Lambda_{16}, preprint available as arXiv:hep-th/9501007.

    Octonions: invariant representation of the Leech lattice, preprint available as arXiv:hep-th/9504040.

    Octonions: invariant Leech lattice exposed, preprint available as arXiv:hep-th/9506080.

week60

  1. N. P. Landsman, Rieffel induction as generalized quantum Marsden-Weinstein reduction, Journal of Geometry and Physics 15 (1995), 285-319.

  2. T. Ohtsuki, Finite type invariants of integral homology 3-spheres, preprint, 1994.

    L. Rozansky, The trivial connection contribution to Witten's invariant and finite type invariants of rational homology spheres, preprint available as arXiv:q-alg/9505015.

    Stavros Garoufalidis, On finite type 3-manifold invariants I, MIT preprint, 1995.

    Stavros Garoufalidis and Jerome Levine, On finite type 3-manifold invariants II, MIT preprint, June 1995. (Garoufalidis is at stavros@math.mit.edu, and Levine is at levine@max.math.brandeis.edu.)

    Ruth J. Lawrence, Asymptotic expansions of Witten-Reshetikhin-Turaev invariants for some simple 3-manifolds, to appear in Jour. Math. Physics.

  3. Thomas Friedrich, Neue Invarianten der 4-dimensionalen Mannigfaltigkeiten, Berlin preprint.

  4. Andre Joyal, Ross Street, and Dominic Verity, Traced monoidal categories, to appear in Math. Proc. Camb. Phil. Soc..

  5. Michael Reisenberger, Worldsheet formulations of gauge theories and gravity, University of Utrecht preprint, 1994, available as arXiv:gr-qc/9412035.

  6. John Baez and Stephen Sawin, Functional integration on spaces of connections, available as arXiv:q-alg/9507023.

  7. John Baez, Javier P. Muniain and Dardo Piriz, Quantum gravity hamiltonian for manifolds with boundary, available as arXiv:gr-qc/9501016.

week61

  1. Alex J. Feingold, Igor B. Frenkel, and John F. X. Rees, Spinor construction of vertex operator algebras, triality, and E8(1), Contemp. Math. 121, AMS, Providence Rhode Island. ISBN 0-8218-5128-4.

  2. Claude Chevalley, The algebraic theory of spinors, Columbia U. Press, New York, 1954.

  3. Ian R. Porteous, Topological Geometry, Cambridge U. Press, Cambridge, 1981.

  4. R. D. Schafer, An Introduction to Non-Associative Algebras, Dover, New York, 1995.

  5. I. L. Kantor and A. S. Solodovnikov, Hypercomplex Numbers -- an Elementary Introduction to Algebras, Springer-Verlag, Berlin, 1989, ISBN 0-387-96980-2 (acid-free paper); ISBN 3-540-96980-2; translation of "Giperkompleksnye chisla", Moscow, 1973.

week62

  1. Victor Guillemin and Shlomo Sternberg, Variations on a Theme by Kepler, American Mathematical Society, Providence, Rhode Island, 1990.

  2. Problems of Present Day Mathematics in Mathematical Developments Arising from Hilbert's Problems, ed. F. E. Browder, Proc. Symp. Pure Math. 28, American Mathematical Society, Providence, Rhode Island, 1976.

  3. M. Hazewinkel, W. Hesselink, D. Siermsa, and F. D. Veldkamp, The ubiquity of Coxeter-Dynkin diagrams (an introduction to the ADE problem), Niew. Arch. Wisk., 25 (1977), 257-307. Also available at http://repos.project.cwi.nl:8888/cwi_repository/docs/I/10/10039A.pdf or http://math.ucr.edu/home/baez/hazewinkel_et_al.pdf

week63

  1. Hermann Weyl, Symmetry, Princeton University Press, Princeton, New Jersey, 1989.

  2. John Frank Adams, Lectures on Lie groups, Benjamin, New York, 1969.

week64

  1. Juergen Fuchs, Affine Lie Algebras and Quantum Groups, Cambridge Monographs on Mathematical Physics, Cambridge U. Press, Cambridge 1992, ISBN 0-521-41593-4.

  2. Victor Kac, Infinite Dimensional Lie Algebras, 3rd ed., Cambridge University Press, Cambridge, 1990.

  3. Loop groups, by Andrew Pressley and Graeme Segal, Oxford University Press, Oxford, 1986.

week65

  1. John H. Conway and Neil J. A. Sloane, Sphere Packings, Lattices and Groups, second edition, Grundlehren der mathematischen Wissenschaften 290, Springer-Verlag, 1993.

  2. Geoffrey Dixon, Octonion X-product and E8 lattices, preprint available as arXiv:hep-th/9411063.

  3. John McKay, Graphs, singularities and finite groups, in Proc. Symp. Pure Math. vol 37, Amer. Math. Soc. (1980), pages 183- and 265-.

    John McKay, Representations and Coxeter Graphs, in "The Geometric Vein" Coxeter Festschrift (1982), Springer-Verlag, Berlin, pages 549-.

    John McKay, A rapid introduction to ADE theory, http://math.ucr.edu/home/baez/ADE.html

  4. Pavel Etinghof and Mikhail Khovanov, Representations of tensor categories and Dynkin diagrams, preprint available as arXiv:hep-th/9408078.

  5. Jurg Froehlich and Thomas Kerler, Quantum Groups, Quantum Categories, and Quantum Field Theory, Springer Lecture Notes in Mathematics 1542, Springer-Verlag, Berlin, 1991.

  6. M. Hazewinkel, W. Hesselink, D. Siermsa, and F. D. Veldkamp, The ubiquity of Coxeter-Dynkin diagrams (an introduction to the ADE problem), Niew. Arch. Wisk., 25 (1977), 257-307.

  7. Capelli and Zuber, Comm. Math. Phys. 113 (1987) 1.

  8. Kato, Mod. Phys. Lett. A2 (1987) 585.

  9. Claude Itzykson and Jean-Michel Drouffe, Statistical Field Theory, 1: From Brownian Motion to Renormalization and Lattice Gauge Theory, and 2: Strong Coupling, Monte Carlo Methods, Conformal Field Theory and Random Systems. Cambridge U. Press, 1989.

week66

  1. The ten billionth hexadecimal digit of pi is 9, by Simon Plouffe, http://groups.google.com/groups?selm=451p8p%24qcr%40morgoth.sfu.ca&output=gplain

  2. David Bailey, Peter Borwein and Simon Plouffe, On the rapid computation of various polylogarithmic constants, available in postscript form from http://www.cecm.sfu.ca/personal/pborwein/PISTUFF/Apistuff.html

  3. The miraculous Bailey-Borwein-Plouffe pi algorithm, by Steven Finch, http://www.lacim.uqam.ca/~plouffe/Simon/Miraculous.pdf

  4. Ron Solomon, On finite simple groups and their classification, AMS Notices Vol. 45, February 1995, 231-239.

  5. Igor Frenkel, James Lepowsky, and Arne Meurman, Vertex Operator Algebras and the Monster, Academic Press, Boston, 1988.

  6. Friedrich Hirzebruch, Thomas Berger, and Rainer Jung, Manifolds and Modular Forms, translated by Peter S. Landweber, pub. Braunschweig, Vieweg, 1992.

  7. Richard E. Borcherds, The Monster Lie-algebra, Adv. Math. 83 (1990), 30-47.

    Richard E. Borcherds, Monstrous Moonshine and monstrous Lie-superalgebras, Invent. Math. 109 (1992), 405-444.

week67

  1. Margaret Wertheim, Pythagoras' Trousers: God, Physics, and the Gender Wars, Times Books/Random House, New York, 1995.

  2. Stephen W. Hawking, Virtual black holes, preprint available as arXiv:hep-th/9510029.

  3. Kerson Huang, Quarks, Leptons, and Gauge Fields, World Scientific Publishing Co., Singapore, 1982. ISBN 9971-950-03-0.

  4. Ted Jacobson, Thermodynamics of spacetime: the Einstein equation of state, preprint available as arXiv:gr-qc/9504004.

  5. Lee Smolin, The Bekenstein bound, topological quantum field theory and pluralistic quantum field theory, preprint available as arXiv:gr-qc/9508064.

  6. Rodolfo Gambini, Octavio Obregon and Jorge Pullin, Towards a loop representation for quantum canonical supergravity, preprint available as arXiv:hep-th/9508036.

  7. Roh Suan Tung and Ted Jacobson, Spinor one-forms as gravitational potentials, preprint available as arXiv:gr-qc/9502037.

  8. Joseph Polchinski and Edward Witten, Evidence for Heterotic - Type I String Duality, preprint available as arXiv:hep-th/9510169.

week68

  1. Robert Goldblatt, Topoi, the Categorial Analysis of Logic, Studies in logic and the foundations of mathematics vol. 98, North-Holland, New York, 1984.

  2. Saunders Mac Lane and Ieke Moerdijk, Sheaves in Geometry and Logic: A First Introduction to Topos Theory, Springer-Verlag, New York, 1992.

  3. Michael Barr and Charles Wells, Toposes, Triples and Theories, Springer-Verlag, New York, 1983. Available for free electronically at http://www.cwru.edu/artsci/math/wells/pub/ttt.html

  4. Frank Close, Are glueballs and hybrids found?, available as arXiv:hep-ph/9509245. To appear in Proceedings of Hadron95.

    J. Sexton, A. Vaccarino, D. Weingarten, Numerical evidence for the observation of a scalar glueball, available as arXiv:hep-lat/9510022.

  5. R. Plaga, Proposal for an experimental test of the many-worlds interpretation of quantum mechanics, preprint available as quant-ph/9510007

  6. Nicholas Landsman, Against the Wheeler-DeWitt equation, preprint available as arXiv:gr-qc/9510033.

  7. Pavel Etingof and David Kazhdan, Quantization of Lie bialgebras, I, preprint available in AMSTeX form as arXiv:q-alg/9506005.

    Quantization of Poisson algebraic groups and Poisson homogeneous spaces, preprint available in AMSTeX form as arXiv:q-alg/9510020.

  8. Steve Carlip, Statistical mechanics and black hole entropy, preprint available as arXiv:gr-qc/9509024.

    Claudio Teitelboim, Statistical thermodynamics of a black hole in terms of surface fields, preprint available as arXiv:hep-th/9510180.

  9. Jorge Griego, Is the third coefficient of the Jones knot polynomial a quantum state of gravity?, preprint available as arXiv:gr-qc/9510051.

    The Kauffman bracket and the Jones polynomial in quantum gravity, preprint available as arXiv:gr-qc/9510050.

week69

  1. Marcia Bartusiak, When the universe began, what time was it?, Technology Review (edited at the Massachusetts Institute of Technology), November/December 1995, pp. 54-63.

  2. C. J. Isham, Structural issues in quantum gravity, plenary session lecture given at the GR14 conference, Florence, August 1995, preprint available as arXiv:gr-qc/9510063.

  3. Abhay Ashtekar, Polymer geometry at Planck scale and quantum Einstein equations.

  4. Renate Loll, Spectrum of the volume operator in quantum gravity, 14 pages in plain tex, with 4 figures (postscript, compressed and uu-encoded), available as arXiv:gr-qc/9511030.

week70

  1. Basic Research Institute in the Mathematical Sciences, New Connections web page, http://www-uk.hpl.hp.com/brims/

  2. A. C. Elitzur and L. Vaidman, Quantum mechanical interaction-free measurements, Foundations of Phys. 23 (1993), 987-997.

    Graeme Mitchison and Richard Jozsa, Counterfactual quantum computation, Proc. Roy. Soc. Lond. A457 (2001) 1175-1194. Also available as quant-ph/9907007.

  3. Jean-Yves Girard, Linear logic, Theoretical Computer Science 50, 1-102, 1987.

    Jean-Yves Girard, Y. Lafont and P. Taylor, Proofs and Types, Cambridge Tracts in Theoretical Computer Science 7, Cambridge U. Press, 1989. Also available at http://www.cs.man.ac.uk/~pt/stable/Proofs+Types.html

  4. Eric Goubault, Schedulers as abstract interpretations of Higher-Dimensional Automata, in Proc. PEPM '95 (La Jolla), ACM Press, 1995. Also available at http://www.di.ens.fr/%7Egoubault/GOUBAULTpapers.html

    Eric Goubault and Thomas Jensen, Homology of higher-dimensional automata, in Proc. CONCUR '92 (New York), Lecture Notes in Computer Science 630, Springer, 1992. Also available at http://www.di.ens.fr/%7Egoubault/GOUBAULTpapers.html

  5. Vaughan Pratt, Time and information in sequential and concurrent computation, Proc. Theory and Practice of Parallel Programming, Sendai, Japan, 1994.

  6. Craig C. Squier, Word problems and a homological finiteness condition for monoids, Jour. Pure Appl. Algebra 49 (1987), 201-217.

    Craig C. Squier, A finiteness condition for rewriting systems, revision by F. Otto and Y. Kobayashi, to appear in Theoretical Computer Science.

    Craig C. Squier and F. Otto, The word problem for finitely presented monoids and finite canonical rewriting systems, in J. P. Jouannuad (ed.), Rewriting Techniques and Applications, Lecture Notes in Computer Science 256 (1987), 74-82.

  7. Yves Lafont and Alain Proute, Church-Rosser property and homology of monoids, to appear in Mathematical Structures in Computer Science.

    Yves Lafont and Alain Proute, Church-Rosser property and homology of monoids, Mathematical Structures in Computer Science 1 (1991), 297-326. Also available at http://iml.univ-mrs.fr/~lafont/publications.html

    Yves Lafont, A new finiteness condition for monoids presented by complete rewriting systems (after Craig C. Squier), Journal of Pure and Applied Algebra 98 (1995), 229-244. Also available at http://iml.univ-mrs.fr/~lafont/publications.html

week71

  1. John Baez and James Dolan, n-Categories, sketch of a definition, http://math.ucr.edu/home/baez/ncat.def.html

  2. Erik Verlinde, Global aspects of electric-magnetic duality, Nuc. Phys. B455 (1995), 211-225, preprint available as arXiv:hep-th/9506011.

    George Thompson, New results in topological field theory and abelian gauge theory, 64 pages, preprint available as arXiv:hep-th/9511038.

  3. Thomas Thiemann, An account of transforms on (A/G)^bar, preprint available as arXiv:gr-qc/9511049.

    Thomas Thiemann, Reality conditions inducing transforms for quantum gauge field theory and quantum gravity, preprint available as arXiv:gr-qc/9511057.

    Abhay Ashtekar, A generalized Wick transform for gravity, preprint available as arXiv:gr-qc/9511083.

    Renate Loll, Making quantum gravity calculable, preprint available as arXiv:gr-qc/9511080.

    Rodolfo Gambini and Jorge Pullin, A rigorous solution of the quantum Einstein equations, preprint avilable in RevTex form as arXiv:gr-qc/9511042, four figures included with epsf.

  4. Matt Greenwood and Xiao-Song Lin, On Vassiliev knot invariants induced from finite type, 14 pages in AMSLaTeX format available as arXiv:q-alg/9506001, with 9 figures not included. The compressed archive of the amslatex file and 9 postscript figure files can be obtained at ftp://math.columbia.edu/pub/lin/gl.tar.Z

    Lev Rozansky, On finite type invariants of links and rational homology spheres derived from the Jones polynomial and Witten- Reshetikhin-Turaev invariant, preprint available as arXiv:q-alg/9511025.

    Scott Axelrod, Overview and warmup example for perturbation theory with instantons, preprint available as arXiv:hep-th/9511196.

  5. Alan Carey, Jouko Mickelsson, and Michael Murray, Index theory, gerbes, and Hamiltonian quantization, 16 pages in Plain TeX (inputting AMSTeX), preprint available as arXiv:hep-th/9511151.

    Alan Carey, M. K. Murray and B. L. Wang, Higher bundle gerbes and cohomology classes in gauge theories, preprint available as arXiv:hep-th/9511169

  6. Jean-Luc Brylinski, Holomorphic gerbes and the Beilinson regulator, in Proc. Int. Conf. on K-Theory (Strasbourg, 1992), to appear in Asterisque.

    Jean-Luc Brylinski and D. A. McLaughlin, The geometry of degree-four characteristic classes and of line bundles on loop spaces I, Duke Math. Jour. 75 (1994), 603-638.

    Jean-Luc Brylinski and D. A. McLaughlin, Cech cocyles for characteristic classes.

  7. Joe Polchinski, Recent results in string duality, preprint available as arXiv:hep-th/9511157, uses PTPTeX.sty.

  8. Leonard Susskind and John Uglum, String physics and black holes, preprint available as arXiv:hep-th/9511227, needs espcrc2.sty.

  9. Boguslaw Broda, A gauge-field approach to 3- and 4-manifold invariants, preprint available in TeX form as arXiv:q-alg/9511010.

  10. John Baez and Martin Neuchl, Higher-dimensional algebra I: braided monoidal 2-categories, available as arXiv:q-alg/9511013.

week72

  1. Kelly Jay Davis, M-Theory and String-String Duality, 28 pages, preprint available as arXiv:hep-th/9601102, uses harvmac.tex.

  2. Edward Witten, Five-branes and M-Theory On An Orbifold, preprint available as arXiv:hep-th/9512219.

  3. Abhay Ashtekar, Polymer geometry at Planck scale and quantum Einstein equations, preprint available as arXiv:hep-th/9601054.

    Roumen Borissov, Seth Major and Lee Smolin, The geometry of quantum spin networks, preprint available as arXiv:gr-qc/9512043, 35 Postscript figures, uses epsfig.sty.

    Bernd Bruegmann, On the constraint algebra of quantum gravity in the loop representation, preprint available as arXiv:gr-qc/9512036.

    Kiyoshi Ezawa, Nonperturbative solutions for canonical quantum gravity: an overview, preprint available as arXiv:gr-qc/9601050

    Kiyoshi Ezawa, A semiclassical interpretation of the topological solutions for canonical quantum gravity, preprint available as arXiv:gr-qc/9512017.

    Jorge Griego, Extended knots and the space of states of quantum gravity, preprint available as arXiv:gr-qc/9601007.

    Seth Major and Lee Smolin, Quantum deformation of quantum gravity, preprint available as arXiv:gr-qc/9512020.

  4. Thomas Kerler, Genealogy of nonperturbative quantum-invariants of 3-manifolds: the surgical family, preprint available as arXiv:q-alg/9601021.

week73

  1. Biological Asymmetry and Handedness, Ciba Foundation Symposium 162, John Wiley and Sons, 1991.

    D. K. Kondepudi and D. K. Nelson, Weak neutral currents and the origins of molecular chirality, Nature 314, pp. 438-441.

  2. N. Hirokawa, Y. Tanaka, Y. Okada and S. Takeda, Nodal flow and the generation of left-right asymmetry, Cell 125 1 (2006), 33-45.

week74

  1. John Baez et al, General relativity tutorial, http://math.ucr.edu/home/baez/gr/gr.html

  2. Abhay Ashtekar and Jerzy Lewandowski, Quantum Theory of Geometry I: Area Operators, 31 pages, to appear in Classical and Quantum Gravity, preprint available as arXiv:gr-qc/9602046.

    Jerzy Lewandowski, Volume and Quantizations, preprint available as arXiv:gr-qc/9602035.

    Roberto De Pietri and Carlo Rovelli, Geometry Eigenvalues and Scalar Product from Recoupling Theory in Loop Quantum Gravity, 38 pages, 5 Postscript figures, uses RevTeX 3.0 and epsfig.sty, preprint available as arXiv:gr-qc/9602023.

  3. Alan Weinstein, Groupoids: unifying internal and external symmetry, available as http://math.berkeley.edu/~alanw/Groupoids.ps

week75

  1. J. P. May, Simplicial Objects in Algebraic Topology, Van Nostrand, Princeton, 1968.

week76

  1. Relativistic Heavy Ion Collider homepage, http://www.rhic.bnl.gov/~rhicb/rhic_home/RHIC.html

    Phase diagram of nuclear matter and nuclear collisions, http://www.rhic.bnl.gov/~rhicb/GIF/9508pdg.gif

  2. Adriano Di Giacomo, Mechanisms of colour confinement, preprint available as arXiv:hep-th/9603029.

week77

  1. Center for Gravitational Physics and Geometry (CGPG) home page, http://vishnu.nirvana.phys.psu.edu/

    Reading list on the new variables: http://vishnu.nirvana.phys.psu.edu/readinglist/readinglist.html

  2. Rodolfo Gambini and Jorge Pullin, The general solution of the quantum Einstein equations?, preprint in Revtex format, 7 figures included with psfig, available as arXiv:gr-qc/9603019.

week78

  1. Higher algebraic structures and quantization, by Daniel Freed, Commun. Math. Phys. 159 (1994), 343-398, also available as arXiv:hep-th/9212115.

week79

  1. Bertram Kostant, The graph of the truncated icosahedron and the last letter of Galois, Notices of the AMS, 959-968 (42), September 1995. Also available as http://www.ams.org/publications/notices/199509/kostant.html

  2. John Baez, Some thoughts on the number 6, http://math.ucr.edu/home/baez/six.html

  3. P. W. Fowler and D. E. Manolpoulos, An Atlas of Fullerenes, Oxford University Press, 1995.

    M. S. Dresselhaus, G. Dresselhaus, and P. C. Eklund, Science of Fullerenes and Carbon Nanotubules, Academic Press, New York, 1994.

    G. Chung, B. Kostant and S. Sternberg, Groups and the buckyball, in Lie Theory and Geometry, eds. J.-L. Brylinski, R. Brylinski, V. Guillemin and V. Kac, Birkhauser, 1994.

  4. Southern Chemical Group homepage, http://www.southchem.com/index.html

week80

  1. Huw Price, Time's Arrow and Archimedes' Point: New Directions for a Physics of Time, Oxford University Press, 1996.

  2. Stephen Hawking and Roger Penrose, The Nature of Space and Time, Princeton University Press, 1996.

  3. Charles Misner, Kip Thorne and John Wheeler, Gravitation, Freeman Press, 1973.

  4. Ignazio Ciufolini and John Archibald Wheeler, Gravitation and Inertia, Princeton University Press, 1995.

  5. Kip Thorne, Richard Price and Douglas Macdonald, eds., Black Holes: The Membrane Paradigm, 1986.

  6. Gravity Probe B, http://www-leland.stanford.edu/~michman/RELATIVITYmosaic/GPBmosaic/GPB.html

  7. LIGO project home page, http://www.ligo.caltech.edu/

  8. Ross Street, Categorical structures, in Handbook of Algebra, vol. 1, ed. M. Hazewinkel, Elsevier, 1996.

  9. G. Maxwell Kelly and Ross Street, Review of the elements of 2-categories, Springer Lecture Notes in Mathematics 420, Berlin, 1974, pp. 75-103.

week81

  1. D. J. Bird et al, Detection of a cosmic ray with measured energy well beyond the expected spectral cutoff due to cosmic microwave radiation, preprint available as arXiv:astro-ph/9410067

    P. Bhattacharjee and G. Sigl, Monopole annihilation and highest energy cosmic rays, preprint available as arXiv:astro-ph/9412053.

    R. J. Protheroe and P. A. Johnson, Are topological defects responsible for the 300 EeV cosmic rays?, preprint available as arXiv:astro-ph/9605006.

  2. Jean-Luc Brylinski and Dennis A. McLaughlin, The geometry of degree four characteristic classes and of line bundles on loop spaces II, preprint.

    Jean-Luc Brylinski, Central extensions and reciprocity laws, preprint.

    Jean-Luc Brylinski, Coadjoint orbits of central extensions of gauge groups, preprint.

    Jean-Luc Brylinski and Dennis A. McLaughlin, The geometry of two dimensional symbols, preprint.

week82

  1. Advances in Applied Clifford Algebras, ed. Jaime Keller. (Subscriptions are available from Mrs. Irma Aragon, F. Q., UNAM, Apartado 70-528, 04510 Mexico, D.F., MEXICO, for US $10 per year.)

  2. H. Blaine Lawson, Jr. and Marie-Louise Michelson, "Spin Geometry", Princeton U. Press, Princeton, 1989.

  3. Dale Husemoller, "Fibre Bundles", Springer-Verlag, Berlin, 1994.

  4. Ralph L. Cohen, John D. S. Jones, and Graeme B. Segal, Morse theory and classifying spaces, preprint as of Sept. 13, 1991.

  5. Graeme B. Segal, Classifying spaces and spectral sequences, Pub. IHES 34 (1968), 105-112.

  6. Ross Street, Descent theory, preprint of talks given at Oberwolfach, Sept. 17-23, 1995.

    Ross Street, Fusion operators and cocycloids in monoidal categories, preprints.

  7. Viqar Husain, Intersecting-loop solutions of the hamiltonian constraint of quantum general relativity, Nucl. Phys. B313 (1989), 711-724.

    Viqar Husain and Karel V. Kuchar, General covariance, new variables, and dynamics without dynamics, Phys. Rev. D 42 (1990), 4070-4077.

    Viqar Husain, Einstein's equations and the chiral model, to appear in Phys. Rev. D, preprint available as gr-qc/9602050.

  8. The Interface of Knots and Physics, ed. Louis H. Kauffman, Proc. Symp. Appl. Math. 51, American Mathematical Society, Providence, Rhode Island, 1996. Contains:

    Louis H. Kauffman, Knots and statistical mechanics

    Ruth J. Lawrence, An introduction to topological field theory

    Dror Bar-Natan, Vassiliev and quantum invariants of braids

    Samuel J. Lomonaco, The modern legacies of Thomson's atomic vortex theory in classical electrodynamics

    John C. Baez, Spin networks in nonperturbative quantum gravity

week83

  1. Alain Connes, Gravity coupled with matter and the foundation of non-commutative geometry, preprint available as arXiv:hep-th/9603053.

    Ali H. Chamseddine and Alain Connes, The spectral action principle, preprint available as arXiv:hep-th/9606001.

  2. Francis Borceux, Handbook of Categorical Algebra, Cambridge U. Press 1994. Volume 1: Basic Category Theory. Volume 2: Categories and Structure. Volume 3: Categories of Sheaves.

week84

  1. AltaVista, http://www.altavista.digital.com/

  2. CYC project homepage, http://www.cyc.com/

  3. Douglas B. Lenat and R.V. Guha, Building Large Knowledge-Based Systems: Representation and Inference in the Cyc Project, Addison-Wesley, Reading, Mass., 1990.

  4. Vaughan Pratt, CYC Report, http://boole.stanford.edu/pub/cyc.report

  5. Project Xanadu, http://xanadu.net/the.project

  6. Ted Kaehler's backlinks browser, http://www.foresight.org/backlinks1.3.1.html

  7. Backlinking news at the Foresight Institute, http://www.foresight.org/backlinks.news.html

    Robin Hanson's ideas on backlinking, http://www.hss.caltech.edu/~hanson/findcritics.html

  8. Francesco Fucito, Maurizio Martellini and Mauro Zeni, The BF formalism for QCD and quark confinement, preprint available as arXiv:hep-th/9605018.

  9. Ioannis Tsohantjis, Alex C. Kalloniatis, and Peter D. Jarvis, Chord diagrams and BPHZ subtractions, preprint available as arXiv:hep-th/9604191.

  10. Masaki Kashiwara and Yoshihisa Saito, Geometric construction of crystal bases, arXiv:q-alg/9606009.

week85

  1. Troy Schilling, Non-covariance of the generalized holonomies: Examples, preprint available as arXiv:gr-qc/9503064.

  2. Thomas Thiemann, Quantum Spin Dynamics (QSD), preprint available as arXiv:gr-qc/9606089.

    Thomas Thiemann, Quantum Spin Dynamics (QSD) II, preprint available as arXiv:gr-qc/9606090.

    Thomas Thiemann, Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity, to appear in Physics Letters B, preprint available as arXiv:gr-qc/9606088.

    Thomas Thiemann, Closed formula for the matrix elements of the volume operator in canonical quantum gravity, preprint available as arXiv:gr-qc/9606091.

    Thomas Thiemann, A length operator for canonical quantum gravity, preprint available as arXiv:gr-qc/9606092.

  3. Kirill Krasnov, Quantum loop representation for fermions coupled to Einstein-Maxwell field, Phys. Rev. D53 (1996), 1874; preprint available as arXiv:gr-qc/9506029.

  4. Carlo Rovelli and Hugo Morales-Tecotl, Fermions in quantum gravity, Phys. Rev. Lett. 72 (1994), 3642-3645.

    Carlo Rovelli and Hugo Morales-Tecotl, Nucl. Phys. B451 (1995), 325, preprint available as arXiv:gr-qc/9401011.

week86

  1. Discreteness of area and volume in quantum gravity, by Carlo Rovelli and Lee Smolin, 36 pages, available as arXiv:gr-qc/9411005.

    Abhay Ashtekar and Jerzy Lewandowski, Quantum theory of geometry I: area operators, 31 pages, to appear in the Classical and Quantum Gravity special issue dedicated to Andrzej Trautman, preprint available as arXiv:gr-qc/9602046.

  2. Junichi Iwasaki, A reformulation of the Ponzano-Regge quantum gravity model in terms of surfaces, University of Pittsburgh, preprint available as arXiv:gr-qc/9410010.

  3. Michael Reisenberger, Worldsheet formulations of gauge theories and Gravity, University of Utrecht preprint, 1994, available as arXiv:gr-qc/9412035.

  4. Renate Loll, The volume operator in discretized quantum gravity, preprint available as arXiv:gr-qc/9506014, 15 pages.

    Renate Loll, Spectrum of the volume operator in quantum gravity, preprint available as arXiv:gr-qc/9511030, 14 pages.

  5. Jerzy Lewandowski, Volume and quantizations, preprint available as arXiv:gr-qc/9602035, 8 pages.

    Abhay Ashtekar and Jerzy Lewandowski, Quantum theory of geometry II: volume operators, manuscript in preparation.

week87

  1. G. Scharf, Finite quantum electrodynamics: the causal approach, Springer-Verlag, Berlin, 1995.

  2. J. F. Colombeau, "Multiplication of Distributions: a Tool in Mathematics, Numerical Engineering, and Theoretical Physics," Lecture Notes in Mathematics 1532, Springer, Berlin, 1992.

  3. Carlo Rovelli, Loop quantum gravity and black hole physics, preprint available as arXiv:gr-qc/9608032.

    Kirill Krasnov, The Bekenstein bound and non-perturbative quantum gravity, preprint available as arXiv:gr-qc/9603025.

    Kirill Krasnov, On statistical mechanics of gravitational systems, preprint available as arXiv:gr-qc/9605047.

  4. Gary Horowitz, The origin of black hole entropy in string theory, preprint available as arXiv:gr-qc/9604051.

    Gary T. Horowitz and Donald Marolf, Counting states of black strings with traveling waves, preprint available as arXiv:hep-th/9605224.

    Gary T. Horowitz and Donald Marolf, Counting states of black strings with traveling waves II, preprint available as arXiv:hep-th/9606113.

  5. Hugo Fort, Rodolfo Gambini and Jorge Pullin, Lattice knot theory and quantum gravity in the loop representation, preprint available as arXiv:gr-qc/9608033.

week88

  1. John Baez, The Hamiltonian constraint in the loop representation of quantum gravity, preprint available in LaTeX form at http://math.ucr.edu/home/baez/hamiltonian/. A less technical version of this appears in Jorge Pullin's newsletter Matters of Gravity, issue 8, at http://www.phys.lsu.edu//mog/mog8/node7.html.

  2. Ted Jacobson, 1+1 sector of 3+1 gravity, Class. Quant. Grav. 13 (1996), L1-L6.

    Peter Schaller and Thomas Strobl, A brief introduction to Poisson sigma-models, preprint available as arXiv:hep-th/9507020.

    Peter Schaller and Thomas Strobl, Poisson sigma-models: a generalization of 2d gravity-Yang-Mills systems, preprint available as arXiv:hep-th/9411163.

week89

  1. Jorge Pullin, ed., Matters of Gravity, first 8 issues now available at http://www.phys.lsu.edu//mog, or latest issue at arXiv:gr-qc/9609008.

  2. MacCallum's gravity mailing list: to subscribe send polite email to M.A.H.MacCallum@qmw.ac.uk

  3. Erwin Schroedinger Institute preprint archive, available at http://www.esi.ac.at/ESI-Preprints.html. Recent preprints include:

    Abhay Ashtekar and Alejandro Corichi, Photon inner-product and the Gauss linking number.

    Abhay Ashtekar, Donald Marolf, Jose Mourao and Thomas Thiemann, SU(N) quantum Yang-Mills theory in 2 dimensions: a complete solution.

    Hugo Fort, Rodolfo Gambini and Jorge Pullin, Lattice knot theory and quantum gravity in the loop representation, also available as arXiv:gr-qc/9608033.

    Michael Reisenberger, A left-handed simplicial action for Euclidean GR.

    Carlo Rovelli, Loop quantum gravity and black hole physics.

  4. Jerzy Lewandowski and Jacek Wilsniewski, 2+1 sector of 3+1 gravity, preprint available as arXiv:gr-qc/9609019.

  5. Lee Smolin, The classical limit and the form of the Hamiltonian constraint in nonperturbative quantum gravity, preprint available as arXiv:gr-qc/9609034.

  6. Lee Smolin, Three dimensional strings as collective coordinates of four dimensional quantum gravity, preprint available as arXiv:gr-qc/9609031.

  7. Michael Dine, String theory dualities, preprint available as arXiv:hep-th/9609051.

  8. John Baez and Martin Neuchl, Higher-dimensional algebra I: braided monoidal 2-categories, available as arXiv:q-alg/9511013.

  9. Categories for the Working Mathematician, by Saunders Mac Lane, Springer, Berlin, 1988.

  10. Ross Street, Categorical structures, in Handbook of Algebra, vol. 1, ed. M. Hazewinkel, Elsevier, 1996.

week90

  1. Claude C. Chevalley, The algebraic theory of spinors, Columbia University Press, New York, 1954.

  2. F. Reese Harvey, Spinors and Calibrations, Academic Press, Boston, 1990.

  3. Ian R. Porteous, Topological geometry, 2nd ed., Cambridge University Press, Cambridge, 1981.

  4. Ian R. Porteous, Clifford algebras and the classical groups, Cambridge University Press, Cambridge, 1995.

  5. Hans Freudenthal and H. de Vries, Linear Lie groups, Academic Press, New York, 1969.

  6. Alex J. Feingold, Igor B. Frenkel, and John F. X. Rees, Spinor construction of vertex operator algebras, triality, and E_8^{(1)}, Contemp. Math. 121, AMS, Providence Rhode Island, ISBN 0-8218-5128-4.

week91

  1. John H. Conway and Neil J. A. Sloane, Sphere Packings, Lattices and Groups, second edition, Grundlehren der mathematischen Wissenschaften 290, Springer-Verlag, 1993.

  2. Frank D. (Tony) Smith, Sets and C^n; quivers and A-D-E; triality; generalized supersymmetry; and D4-D5-E6, preprint available as arXiv:hep-th/9306011.

  3. Tony Smith's home page, http://www.innerx.net/personal/tsmith/TShome.html

  4. Hans Freudenthal, Adv. Math. 1 (1964) 143.

  5. Jacques Tits, Indag. Math. 28 (1966) 223-237.

  6. Kevin McCrimmon, Jordan Algebras and their Applications, Bull. AMS 84 (1978) 612-627, at pp. 620-621

  7. Tony Smith, Freudenthal-Tits magic square, http://www.innerx.net/personal/tsmith/FTsquare.html

week92

  1. Applications of negative dimensional tensors, by Roger Penrose, in Combinatorial Mathematics and its Applications, ed. D. J. A. Welsh, Academic Press, 1971.

  2. Sidney Coleman, Aspects of Symmetry, Cambridge University Press, 1989. ISBN 0 521 26706 4 (hardback) and ISBN 0 521 31827 0 (paperback).

  3. Dror Bar-Natan, Lie algebras and the four color theorem, preprint available as arXiv:q-alg/9606016.

  4. Neil Robertson, Daniel P. Sanders, Paul Seymour, and Robin Thomas, A new proof of the four-colour theorem, Electronic Research Announcements of the American Mathematical Society 2 (1996), 17-25. Available at http://www.ams.org/journals/era/1996-02-01/

week93

  1. Paul Langacker, Implications of neutrino mass, http://dept.physics.upenn.edu/neutrino/jhu/jhu.html

  2. John Baez, Spin, statistics, CPT and all that jazz, http://math.ucr.edu/home/baez/spin.stat.html

  3. John H. Schwarz, Introduction to supersymmetry, in Superstrings and Supergravity, Proc. of the 28th Scottish Universities Summer School in Physics, ed. A. T. Davies and D. G. Sutherland, University Printing House, Oxford, 1985.

  4. John H. Schwarz, Introduction to superstrings, in Superstrings and Supergravity, Proc. of the 28th Scottish Universities Summer School in Physics, ed. A. T. Davies and D. G. Sutherland, University Printing House, Oxford, 1985.

week94

  1. Frank Wilczek, Asymptotic freedom, preprint available as arXiv:hep-th/9609099.

  2. N. K. Nielsen, Am. J. Phys. 49, 1171 (1981).

  3. R. J. Hughes, Nucl. Phys. B186, 376 (1981).

  4. Richard Feynman, Robert Leighton, and Matthew Sands, "The Feynman Lectures on Physics", Addison-Wesley, Reading, Mass., 1964.

  5. Barry Simon, "Functional Integration and Quantum Physics ", Academic Press, 1979.

week95

  1. Laurie M. Brown, ed., "Renormalization: From Lorentz to Landau (and Beyond)", Springer-Verlag, New York, 1993. ISBN 0-387-97933-6, ISBN 3-540-97933-6.

  2. W. S. Anglin, "The Queen of Mathematics: An Introduction to Number Theory", Kluwer, Dordrecht, 1995. ISBN 0-7923-3287-3.

    W. S. Anglin, American Mathematical Monthly, February 1990, pp. 120-124.

  3. Jet Wimp, Eight recent mathematical books, Math. Intelligencer 18 (1996), 72-79.

  4. John Baez, Spin and the harmonic oscillator, http://math.ucr.edu/home/baez/harmonic.html

  5. David J. Gross, The heterotic string, in "Workshop on Unified String Theories", eds. M. Green and D. Gross, World Scientific, Singapore, 1986, pp. 357-399.

  6. Edward Witten, Unification in ten dimensions, in "Workshop on Unified String Theories", eds. M. Green and D. Gross, World Scientific, Singapore, 1986, pp. 438-456.

    Edward Witten, Topological tools in ten dimensional physics, with an appendix by R. E. Stong, in "Workshop on Unified String Theories", eds. M. Green and D. Gross, World Scientific, Singapore, 1986, pp. 400-437.

  7. Reinhold W. Gebert and Hermann Nicolai, E10 for beginners, preprint available as arXiv:hep-th/9411188

  8. Gregory Moore, Finite in all directions, preprint available as arXiv:hep-th/9305139.

  9. Reinhold W. Gebert, Introduction to vertex algebras, Borcherds algebras, and the Monster Lie algebra, preprint available as arXiv:hep-th/9308151.

  10. Igor Frenkel, James Lepowsky, and Arne Meurman, "Vertex Operator Algebras and the Monster," Academic Press, 1988.

  11. Richard Borcherds, Automorphic forms and Lie algebras.

    Richard Borcherds, Sporadic groups and string theory.

    These and other papers available at http://www.pmms.cam.ac.uk/Staff/R.E.Borcherds.html; click on the personal home page.

  12. P. West, E11 and M-theory, available as arXiv:hep-th/0104081.

week96

  1. J. Scott Carter, Daniel E. Flath and Masahico Saito, "The Classical and Quantum 6j-Symbols", Princeton University Press, Princeton, 1995. ISBN 0-691-02730-7.

  2. E. Guadagnini, L. Pilo, Three-manifold invariants and their relation with the fundamental group, 22 pages, preprint available as arXiv:hep-th/9612090.

  3. Michael Reisenberger and Carlo Rovelli, "Sum over surfaces" form of loop quantum gravity, preprint available as arXiv:gr-qc/9612035.

week97

  1. Spin, statistics, CPT and all that jazz, http://math.ucr.edu/home/baez/spin.stat.html

  2. Physicists create new state of matter, http://jilav1.colorado.edu/www/bose-ein.html

    Atomcool home page, http://atomcool.rice.edu/

    Neutral sodium ion trap at MIT, http://bink.mit.edu/dallin/nat.html

  3. Matter-wave interference of two Bose condensates, http://bink.mit.edu/dallin/news.html#matterwave

  4. Rodolfo Gambini and Jorge Pullin, "Loops, knots, gauge theories, and quantum gravity", Cambridge U. Press, Cambridge, 1996, ISBN 0-521-47332-2.

  5. Gerard 't Hooft, Nucl. Phys. B138, (1978) 1.

  6. Abhay Ashtekar and Alejandro Corichi, Gauss linking number and electro-magnetic uncertainty principle, preprint available as arXiv:hep-th/9701136.

  7. Dror Bar-Natan and Alexander Stoimenow, The fundamental theorem of Vassiliev invariants, preprint available as arXiv:q-alg/9702009.

week98

  1. Kirill Krasnov, On statistical mechanics of Schwarzschild black hole, preprint available as arXiv:gr-qc/9605047.

  2. Maximo Banados and Andres Gomberoff, Black hole entropy in the Chern-Simons formulation of 2+1 gravity, preprint available as arXiv:gr-qc/9611044.

  3. John Baez, Degenerate solutions of general relativity from topological field theory, preprint available as arXiv:gr-qc/9702051 or in Postscript form at http://math.ucr.edu/home/baez/deg.ps.

  4. Neil Ashby, General relativity in the global positioning system, in Matters of Gravity, ed. Jorge Pullin, no. 9, available at http://www.phys.lsu.edu//mog/mog9/node9.html.

  5. "Handbook of Algebraic Topology", ed. I. M. James, North-Holland, the Netherlands, 1995, 1324 pages, ISBN 0-444-81779-4.

week99

  1. Lee Smolin, The future of spin networks, in The Geometric Universe: Science, Geometry, and the Work of Roger Penrose, eds. S. Huggett, Paul Tod, and Lionel J. Mason, Oxford University Press, 1998. Also available as arXiv:gr-qc/9702030.

  2. Roger Penrose, Theory of quantized directions, unpublished manuscript.

  3. Fotini Markopoulou and Lee Smolin, Causal evolution of spin networks, preprint available as arXiv:gr-qc/9702025.

  4. Luca Bombelli, Joohan Lee, David Meyer and Rafael D. Sorkin, Space-time as a causal set, Phys. Rev. Lett. 59 (1987), 521.

  5. Workshop on Higher Category Theory and Physics, March 28-30, 1997, Northwestern University, Evanston, Illinois. Organized by Ezra Getzler and Mikhail Kapranov; program available at http://math.nwu.edu/~getzler/conf97.html

  6. Higher algebraic structures and quantization, by Dan Freed, Comm. Math. Phys. 159 (1994), 343-398, preprint available as arXiv:hep-th/9212115; see also week48.

  7. Louis Crane: Clock and category: is quantum gravity algebraic?, Jour. Math. Phys. 36 (1995), 6180-6193, preprint available as arXiv:gr-qc/9504038.

  8. John Baez, Higher-dimensional algebra II: 2-Hilbert spaces, to appear in Adv. Math., preprint available as arXiv:q-alg/9609018 or at http://math.ucr.edu/home/baez/2hilb.ps.Z

week100

  1. S. Eilenberg and S. Mac Lane, General theory of natural equivalences, Trans. Amer. Math. Soc. 58 (1945), 231-294.

  2. J. Benabou, Introduction to bicategories, Springer Lecture Notes in Mathematics 47, New York, 1967, pp. 1-77.

  3. R. Gordon, A. J. Power, and R. Street, Coherence for tricategories, Memoirs Amer. Math. Soc. 117 (1995) Number 558.

  4. S. E. Crans, On combinatorial models for higher dimensional homotopies, Ph.D. thesis, University of Utrecht, Utrecht, 1991.

  5. Ross Street, The algebra of oriented simplexes, Jour. Pure Appl. Alg. 49 (1987), 283-335.

  6. J. Baez and J. Dolan, n-Categories - sketch of a definition, letter to Ross Street, Nov. 29, 1995, available at http://math.ucr.edu/home/baez/ncat.def.html

  7. J. Baez and J. Dolan, Higher-dimensional algebra III: n-Categories and the algebra of opetopes, to appear in Adv. Math., preprint available as arXiv:q-alg/9702014 and at http://math.ucr.edu/home/baez/op.ps, or in compressed form as http://math.ucr.edu/home/baez/op.ps.Z

  8. Z. Tamsamani, Sur des notions de $\infty$-categorie et $\infty$-groupoide non-strictes via des ensembles multi-simpliciaux, Ph.D. thesis, Universite Paul Sabatier, Toulouse, France, 1995.

  9. M. A. Batanin, On the definition of weak omega-category, Macquarie Mathematics Report number 96/207.

week101

  1. Manfred Eigen, The Hypercycle, a Principle of Natural Self-Organization, Springer-Verlag, Berlin, 1979.

  2. G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems: from Dissipative Structures to Order Through Fluctuations, Wiley, New York, 1977.

    Ilya Prigogine, From Being to Becoming: Time and Complexity in the Physical Sciences, W. H. Freeman, San Francisco, 1980.

    Ilya Prigogine, Introduction to Thermodynamics of Irreversible Processes, 3d ed., Interscience Publishers, New York, 1967.

  3. Stuart A. Kauffman, At Home in the Universe: the Search for Laws of Self-Organization and Complexity, Oxford University Press, New York, 1995.

    Stuart A. Kauffman, The Origins of Order: Self-Organization and Selection in Evolution, Oxford University Press, New York, 1993.

  4. Lee Smolin, The Life of the Cosmos, Crown Press, 1997.

  5. Stuart Kauffman and Lee Smolin, A possible solution to the problem of time in quantum cosmology, preprint available as arXiv:gr-qc/9703026.

  6. Edge: http://www.edge.org

week102

  1. Ulrike Tillmann, The moduli space of Riemann surfaces - a homotopy theory approach, talk at Northwestern University Algebraic Topology Conference, March 27, 1997

  2. Douglas C. Ravenel, Complex cobordism and stable homotopy groups of spheres, Academic Press, Orlando, 1986.

    Douglas C. Ravenel, Nilpotence and periodicity in stable homotopy theory, Princeton University Press, Princeton, 1992.

  3. Higher-dimensional algebra and topological quantum field theory, by John Baez and James Dolan, Jour. Math. Phys. 36 (1995), 6073-6105.

week103

  1. Ronald Brown, Higher-dimensional group theory, http://www.bangor.ac.uk/~mas010/home.html

  2. Symbolic sculptures and mathematics, http://www.bangor.ac.uk/~mas007/welcome.html

  3. Ross Street, The role of Michael Batanin's monoidal globular categories. Lecture I: Globular categories and trees. Lecture II: Higher operads and weak omega-categories. Available in gunzipped Postscript form at http://www.math.mq.edu.au/~street/Publications.html

  4. Michael Batanin, Monoidal globular categories as a natural environment for the theory of weak n-categories, Adv. Math 136 (1998), 39-103, preprint available at http://www-math.mpce.mq.edu.au/~mbatanin/papers.html

  5. John Baez, An introduction to n-categories, to appear in the proceedings of Category Theory and Computer Science '97, preprint available as arXiv:q-alg/9705009 or in Postscript form at http://math.ucr.edu/home/baez/ncat.ps

  6. Zouhair Tamsamani, Sur des notions de $\infty$-categorie et $\infty$-groupoide non-strictes via des ensembles multi-simpliciaux, preprint available as alg-geom/9512006.

    Zouhair Tamsamani, Equivalence de la theorie homotopique des n-groupoides et celle des espaces topologiques n-tronques, preprint available as alg-geom/9607010.

  7. Carlos Simpson, A closed model structure for n-categories, internal Hom, n-stacks and generalized Seifert-Van Kampen, preprint available as alg-geom/9704006.

  8. J. Scott Carter, Joachim H. Rieger and Masahico Saito, A combinatorial description of knotted surfaces and their isotopies, to appear in Adv. Math., preprint available at http://www.math.usf.edu/~saito/home.html

  9. John Baez and Laurel Langford, 2-Tangles, preprint available as arXiv:q-alg/9703033 and in Postscript form at http://math.ucr.edu/home/baez/2tang.ps

  10. J. Scott Carter, Louis H. Kauffman and Masahico Saito, Diagrammatics, singularities, and their algebraic interpretations, preprint available at http://www.math.usf.edu/~saito/home.html

week104

  1. Michael J. Crowe, A History of Vector Analysis, University of Notre Dame, Notre Dame, 1967.

  2. Tony Smith, http://www.innerx.net/personal/tsmith/TShome.html

  3. Geoffrey Dixon, http://www.7stones.com (Warning: to really get into this you need to have at least Netscape 3.0 with Java and Shockwave stuff.)

  4. Corinne A. Manogue and Joerg Schray, Finite Lorentz transformations, automorphisms, and division algebras, Jour. Math. Phys. 34 (1993), 3746-3767.

    Corinne A. Manogue and Joerg Schray, Octonionic representations of Clifford algebras and triality, preprint available as arXiv:hep-th/9407179.

  5. Anthony Sudbery, Division algebras, (pseudo)orthogonal groups and spinors, Jour. Phys. A 17 (1984), 939-955.

    Anthony Sudbery, Seven types of incongruity, handwritten notes.

  6. J. M. Evans, Supersymmetric Yang-Mills theories and division algebras, Nucl. Phys. B298 (1988), 92-108.

week105

  1. The Collected Papers of Raoul Bott, ed. R. D. MacPherson. Vol. 1: Topology and Lie Groups (the 1950s). Vol. 2: Differential Operators (the 1960s). Vol. 3: Foliations (the 1970s). Vol. 4: Mathematics Related to Physics (the 1980s). Birkhauser, Boston, 1994, 2355 pages total.

  2. M. F. Atiyah, R. Bott, and A. Shapiro, Clifford modules, Topology (3) 1964, 3-38.

  3. Dave Rusin, Binary products, algebras, and division rings, http://www.math.niu.edu/~rusin/known-math/95/division.alg

week106

  1. Boris Rosenfeld, Geometry of Lie Groups, Kluwer Academic Publishers, 1997.

  2. John Frank Adams, Lectures on Exceptional Lie Groups, eds. Zafer Mahmud and Mamoru Mimura, University of Chicago Press, Chicago, 1996.

  3. Michael B. Green, John H. Schwarz, and Edward Witten, Superstring Theory, two volumes, Cambridge U. Press, Cambridge, 1987.

  4. V. S. Varadarajan, Geometry of Quantum Theory, Springer-Verlag, Berlin, 2nd ed., 1985.

  5. Stephen L. Adler, Quaternionic Quantum Mechanics and Quantum Fields, Oxford U. Press, Oxford, 1995.

  6. Daniel Allcock, Reflection groups on the octave hyperbolic plane, University of Utah Mathematics Department preprint.

  7. Arthur L. Besse, Einstein Manifolds, Springer, Berlin, 1987, pp. 313-316.

week107

  1. Florian W. J. Weig, Peter V. Coveney, and Bruce M. Boghosian, Lattice- gas simulations of minority-phase domain growth in binary immiscible and ternary amphiphilic fluid, preprint available as cond-mat/9705248.

  2. James Gilliam, Lagrangian and Symplectic Techniques in Discrete Mechanics, Ph.D. thesis, Department of Mathematics, University of Riverside, 1996.

    John Baez and James Gilliam, An algebraic approach to discrete mechanics, Lett. Math. Phys. 31 (1994), 205-212. Also available as http://math.ucr.edu./home/baez/ca.tex

  3. P. R. Kotiuga, Metric dependent aspects of inverse problems and functionals based helicity, Journal of Applied Physics, 70 (1993), 5437-5439.

    Analysis of finite element matrices arising from discretizations of helicity functionals, Journal of Applied Physics, 67 (1990), 5815-5817.

    Helicity functionals and metric invariance in three dimensions, IEEE Transactions on Magnetics, MAG-25 (1989), 2813-2815.

    Variational principles for three-dimensional magnetostatics based on helicity, Journal of Applied Physics, 63 (1988), 3360-3362.

  4. Gerald Jay Sussman and Jack Wisdom, Chaotic evolution of the solar system, Science, 257, 3 July 1992.

    Gerald Jay Sussman and Jack Wisdom, Numerical evidence that the motion of Pluto is chaotic, Science, 241, 22 July 1988.

    James Applegate, M. Douglas, Y. Gursel, Gerald Jay Sussman, Jack Wisdom, The outer solar system for 200 million years, Astronomical Journal, 92, pp 176-194, July 1986, reprinted in Lecture Notes in Physics #267 -- Use of Supercomputers in Stellar Dynamics, Springer Verlag, 1986.

    James Applegate, M. Douglas, Y. Gursel, P Hunter, C. Seitz, Gerald Jay Sussman, A digital orrery, in IEEE Transactions on Computers, C-34, No. 9, pp. 822-831, September 1985, reprinted in Lecture Notes in Physics #267, Springer Verlag, 1986.

  5. John Baez, An introduction to n-categories, to appear in 7th Conference on Category Theory and Computer Science, eds. E. Moggi and G. Rosolini, Springer Lecture Notes in Computer Science vol. 1290, Springer, Berlin. Preprint available as arXiv:q-alg/9705009 or at http://math.ucr.edu/home/baez/ncat.ps

  6. Claudio Hermida, Michael Makkai and John Power, On weak higher dimensional categories, 104 pages, preprint available at http://hypatia.dcs.qmw.ac.uk/authors/M/MakkaiM/papers/multitopicsets/

  7. Michael Batanin, Finitary monads on globular sets and notions of computad they generate, available as postscript files at http://www-math.mpce.mq.edu.au/~mbatanin/papers.html

  8. Carlos Simpson, Limits in n-categories, approximately 90 pages, preprint available as alg-geom/9708010.

  9. Sjoerd Crans, Generalized centers of braided and sylleptic monoidal 2-categories, preprint available at http://www-math.mpce.mq.edu.au/~scrans/papers/papers.html

week108

  1. Eugenio Moggi and Giuseppe Rosolini, eds., Category Theory and Computer Science, Lecture Notes in Computer Science 1290, Springer Verlag, Berlin, 1997.

  2. Michael Reed and Barry Simon, Methods of Modern Mathematical Physics. Vol. 1: Functional Analysis. Vol. 2: Fourier Analysis, Self-Adjointness. Vol. 3: Scattering Theory. Vol. 4: Analysis of Operators. Academic Press, New York, 1980.

  3. Andre Joyal, Une th'eorie combinatoire des s'eries formelles, Advances in Mathematics 42 (1981), 1-82.

  4. N. Chomsky and M. P. Schutzenberger, The algebraic theory of context-free languages, in Computer Programming and Formal Systems, North-Holland Publishing Company, 1963.

  5. Samuel Eilenberg, Automata, Languages and Machines, Academic Press, NY, 1974.

  6. Ole Vilhelm Larsen, Computing order-independent statistical characteristics of stochastic context-free languages, available as http://cwis.auc.dk/phd/fulltext/larsen/html/index.html or acrobat format in: http://cwis.auc.dk/phd/fulltext/larsen/pdf/larsen.pdf

week109

  1. Charles Misner, Kip Thorne and John Wheeler, Gravitation Freeman Press, 1973.

  2. John Wheeler, Geometrodynamics, Academic Press, New York, 1962.

  3. Roger Penrose and Wolfgang Rindler, Spinors and Space-Time. Vol. 1: Two-Spinor Calculus and Relativistic Fields. Vol. 2: Spinor and Twistor Methods in Space-Time Geometry. Cambridge University Press, Cambridge, 1985-1986.

  4. Robert M. Wald, General Relativity, University of Chicago Press, Chicago, 1984.

  5. John Moussouris, Quantum models of space-time based on recoupling theory, Ph.D. thesis, Department of Mathematics, Oxford University, 1983.

  6. Edward Witten, A new proof of the positive energy theorem, Commun. Math. Phys. 80 (1981), 381-402.

week110

  1. Angular momentum; an approach to combinatorial space time, by Roger Penrose, in Quantum Theory and Beyond; ed. T. Bastin, Cambridge University Press, Cambridge, 1971.

  2. Carlo Rovelli, Loop quantum gravity, preprint available as arXiv:gr-qc/9710008, also available as a webpage on Living Reviews in Relativity at http://www.livingreviews.org/lrr-1998-1

  3. Carlo Rovelli's homepage, http://www.phyast.pitt.edu/~rovelli/

  4. Andrea Barbieri, Quantum tetrahedra and simplicial spin networks, preprint available as arXiv:gr-qc/9707010.

  5. C. Nash, Topology and physics - a historical essay, to appear in A History of Topology, edited by Ioan James, Elsevier-North Holland, preprint available as arXiv:hep-th/9709135.

  6. Luis Alvarez-Gaume and Frederic Zamora, Duality in quantum field theory (and string theory), available as arXiv:hep-th/9709180.

  7. Richard E. Borcherds, What is a vertex algebra?, available as arXiv:q-alg/9709033.

  8. J. M. F. Labastida and Carlos Lozano, Lectures in topological quantum field theory, 62 pages, preprint available as arXiv:hep-th/9709192.

  9. Martin Markl, Simplex, associahedron, and cyclohedron, preprint available as alg-geom/9707009.

week111

  1. Roger Penrose, Gravitational collapse: the role of general relativity, Rev. del Nuovo Cimento 1, (1969) 272-276.

  2. Stephen Hawking, Gravitational radiation from colliding black holes, Phys. Rev. Lett. 26 (1971), 1344-1346.

  3. Robert M. Wald, Black holes and thermodynamics, in Symposium on Black Holes and Relativistic Stars (in honor of S. Chandrasekhar), December 14-15, 1996, preprint available as arXiv:gr-qc/9702022.

  4. Jacob Bekenstein, Black holes and entropy, Phys. Rev. D7 (1973), 2333-2346.

  5. Stephen Hawking, Particle creation by black holes, Commun. Math. Phys. 43 (1975), 199-220.

  6. Gary Horowitz, Quantum states of black holes, preprint available as arXiv:gr-qc/9704072.

  7. Roman Jackiw, What is quantum field theory and why have some physicists abandoned it?, 4 pages, preprint available as arXiv:hep-th/9709212.

  8. Adel Bilal, M(atrix) theory: a pedagogical introduction, preprint available as arXiv:hep-th/9710136.

  9. Gregory Gabadadze, Modeling the glueball spectrum by a closed bosonic membrane, 43 pages, preprint available as arXiv:hep-ph/9710402.

  10. Jose M. Figueroa-O'Farrill, Gauge theory and the division algebras, preprint available as arXiv:hep-th/9710168.

week112

  1. Greg Egan, Distress, HarperCollins, 1995.

  2. Abhay Ashtekar, John Baez, Alejandro Corichi and Kirill Krasnov, Quantum geometry and black hole entropy, to appear in Phys. Rev. Lett., preprint available as arXiv:gr-qc/9710007.

  3. Giorgio Immirzi, Quantum gravity and Regge calculus, in Nucl. Phys. Proc. Suppl. 57 (1997) 65-72, preprint available as arXiv:gr-qc/9701052.

  4. Fernando Barbero, Real Ashtekar variables for Lorentzian signature space-times, Phys. Rev. D51 (1995), 5507-5510, preprint available as arXiv:gr-qc/9410014.

  5. Carlo Rovelli and Thomas Thiemann, The Immirzi parameter in quantum general relativity, preprint available as arXiv:gr-qc/9705059.

  6. Kirill Krasnov, On the constant that fixes the area spectrum in canonical quantum gravity, preprint available as arXiv:gr-qc/9709058.

  7. Kirill Krasnov, Quantum geometry and thermal radiation from black holes, preprint available as arXiv:gr-qc/9710006.

  8. Jacob D. Bekenstein and V. F. Mukhanov, Spectroscopy of the quantum black hole, preprint available as arXiv:gr-qc/9505012.

  9. Jun-ichi Igusa, Theta Functions, Springer-Verlag, Berlin, 1972.

  10. David Mumford, Tata Lectures on Theta, 3 volumes, Birkhauser, Boston, 1983-1991.

week113

  1. C. Hog-Angeloni, W. Metzler, and A. Sieradski, Two-dimensional Homotopy and Combinatorial Group Theory, London Mathematical Society Lecture Note Series 197, Cambridge U. Press, Cambridge, 1993.

  2. John Barrett and Louis Crane, Relativistic spin networks and quantum gravity, 9 pages, preprint available as arXiv:gr-qc/9709028.

  3. John Baez, Spin foam models, 39 pages, preprint available as arXiv:gr-qc/9709052 or in Postscript form as http://math.ucr.edu/home/baez/foam.ps

  4. Michael Reisenberger, Worldsheet formulations of gauge theories and gravity, preprint available as arXiv:gr-qc/9412035.

  5. Michael Reisenberger and Carlo Rovelli, ``Sum over surfaces'' form of loop quantum gravity, Phys. Rev. D56 (1997), 3490-3508, preprint available as arXiv:gr-qc/9612035.

  6. Michael Reisenberger, A lattice worldsheet sum for 4-d Euclidean general relativity, 50 pages, preprint available as arXiv:gr-qc/9711052.

  7. Andrea Barbieri, Space of the vertices of relativistic spin networks, 2 pages, preprint available as arXiv:gr-qc/9709076.

  8. Louis Crane, On the interpretation of relativistic spin networks and the balanced state sum, 4 pages, preprint available as arXiv:gr-qc/9710108.

week114

  1. John W. Barrett, Martin Rocek, Ruth M. Williams, A note on area variables in Regge calculus, preprint available as arXiv:gr-qc/9710056.

  2. Jarmo Makela, Variation of area variables in Regge calculus preprint available as arXiv:gr-qc/9801022.

  3. Louis Crane and David N. Yetter, On the classical limit of the balanced state sum, preprint available as arXiv:gr-qc/9712087.

  4. Lee Smolin, Strings as perturbations of evolving spin-networks, preprint available as arXiv:hep-th/9801022.

  5. Fotini Markopoulou and Lee Smolin, Quantum geometry with intrinsic local causality, preprint available as arXiv:gr-qc/9712067.

  6. Abhay Ashtekar and Jerzy Lewandowski, Quantum theory of geometry II: volume operators, preprint available as arXiv:gr-qc/9711031.

  7. Thomas Thiemann, Quantum spin dynamics (QSD), preprint available as arXiv:gr-qc/9606089.

    Quantum spin dynamics (QSD) II, preprint available as arXiv:gr-qc/9606090.

    QSD III: Quantum constraint algebra and physical scalar product in quantum general relativity, preprint available as arXiv:gr-qc/9705017.

    QSD IV: 2+1 Euclidean quantum gravity as a model to test 3+1 Lorentzian quantum gravity, preprint available as arXiv:gr-qc/9705018.

    QSD V: Quantum gravity as the natural regulator of matter quantum field theories, preprint available as arXiv:gr-qc/9705019.

    QSD VI: Quantum Poincare algebra and a quantum positivity of energy theorem for canonical quantum gravity, preprint available as arXiv:gr-qc/9705020

    Kinematical Hilbert spaces for fermionic and Higgs quantum field theories, arXiv:gr-qc/9705021

  8. Jerzy Lewandowski and Donald Marolf, Loop constraints: A habitat and their algebra, preprint available as arXiv:gr-qc/9710016.

  9. Rodolfo Gambini, Jerzy Lewandowski, Donald Marolf, and Jorge Pullin, On the consistency of the constraint algebra in spin network quantum gravity, preprint available as arXiv:gr-qc/9710018.

  10. Steven Carlip, Spacetime foam and the cosmological constant, Phys. Rev. Lett. 79 (1997) 4071-4074, preprint available as arXiv:gr-qc/9708026.

week115

  1. Greg Egan, Diaspora, Orion Books, 1997.

  2. Saunders Mac Lane and Ieke Moerdijk, Sheaves in Geometry and Logic: a First Introduction to Topos Theory, Springer-Verlag, New York, 1992.

  3. Saunders Mac Lane, Categories for the Working Mathematician, Springer, Berlin, 1988.

  4. J. Peter May, Simplicial Objects in Algebraic Topology, Van Nostrand, Princeton, 1968.

week116

  1. Lochlainn O'Raifeartaigh, The Dawning of Gauge Theory, Princeton U. Press, Princeton, 1997.

  2. Henri Cartan and Samuel Eilenberg, Homological Algebra, Princeton University Press, 1956.

  3. Saunders Mac Lane, Homology, Springer-Verlag, Berlin, 1995.

  4. Joseph J. Rotman, An Introduction to Homological Algebra, Academic Press, New York, 1979.

  5. Marvin J. Greenberg, John R. Harper, Algebraic Topology: A First Course, Benjamin/Cummings, Reading, Massachusetts, 1981.

  6. William S. Massey, Singular Homology Theory, Springer-Verlag, New York, 1980.

week117

  1. The E864 Collaboration, Search for charged strange quark matter produced in 11.5 A GeV/c Au + Pb collisions, Phys. Rev. Lett. 79 (1997) 3612-3616, preprint available as nucl-ex/9706004.

  2. Juergen Eschke, NA35 Collaboration, Strangeness enhancement in sulphur- nucleus collisions at 200 GeV/N, preprint available as arXiv:hep-ph/9609242.

  3. E. P. Gilson and R. L. Jaffe, Very small strangelets, Phys. Rev. Lett. 71 (1993) 332-335, preprint available as arXiv:hep-ph/9302270.

  4. Edward Witten, Cosmic separation of phases, Phys. Rev. D30 (1984) 272-285.

  5. Dany Page, Strange stars: Which is the ground state of QCD at finite baryon number?, `High Energy Phenomenology' eds. M. A. Perez & R. Huerta (World Scientific), 1992, pp. 347 - 356, preprint available as arXiv:astro-ph/9602043.

  6. Strange Quark Matter in Physics and Astrophysics: Proceedings of the International Workshop on Strange Quark Matter in Physics and Astrophysics, ed. Jes Madsen, North-Holland, Amsterdam, 1991.

  7. International Symposium on Strangeness and Quark Matter, eds. Georges Vassiliadis et al, World Scientific, Singapore, 1995.

  8. Graeme B. Segal, Classifying spaces and spectral sequences, Publ. Math. Inst. des Haut. Etudes Scient. 34 (1968), 105-112.

week118

  1. Michael J. Duff, The theory formerly known as strings, Scientific American 278 (February 1998), 64-69.

  2. M. J. Duff, Supermembranes, preprint available as arXiv:hep-th/9611203

  3. Michael B. Green, John H. Schwarz, and Edward Witten, Superstring Theory, two volumes, Cambridge U. Press, Cambridge, 1987.

  4. Bryce DeWitt, Supermanifolds, Cambridge U. Press, Cambridge, 2nd edition, 1992.

  5. E. Corrigan and T. J. Hollowood, The exceptional Jordan algebra and the superstring, Commun. Math. Phys., 122 (1989), 393.

  6. E. Corrigan and T. J. Hollowood, A string construction of a commutative nonassociative algebra related to the exceptional Jordan algebra, Phys. Lett. B203 (1988), 47.

  7. Y. Tanii, Introduction to supergravities in diverse dimensions, preprint available as arXiv:hep-th/9802138.

  8. Stephan Melosch and Hermann Nicolai, New canonical variables for d = 11 supergravity, preprint available as arXiv:hep-th/9709277.

  9. G. Sierra, An application of the theories of Jordan algebras and Freudenthal triple systems to particles and strings, Class. Quant. Grav. 4 (1987), 227.

  10. J. M. Evans, Supersymmetric Yang-Mills theories and division algebras, Nucl. Phys. B298 (1988), 92-108.

  11. W. Lerche, Recent developments in string theory, preprint available as arXiv:hep-th/9710246.

  12. John Schwarz, The status of string theory, preprint available as arXiv:hep-th/9711029.

  13. M. J. Duff, M-theory (the theory formerly known as strings), preprint available as arXiv:hep-th/9608117.

week119

  1. Edward Witten, Grand unification with and without supersymmetry, Introduction to supersymmetry in particle and nuclear physics, edited by O. Castanos, A. Frank, L. Urrutia, Plenum Press, 1984.

  2. Graham G. Ross, Grand Unified Theories, Benjamin-Cummings, 1984.

  3. Ranindra N. Mohapatra, Unification and Supersymmetry: The Frontiers of Quark-Lepton Physics, Springer-Verlag, 1992.

  4. D. V. Nanopoulos, Tales of the GUT age, in Grand Unified Theories and Related Topics, proceedings of the 4th Kyoto Summer Institute, World Scientific, Singapore, 1981.
  5. P. Ramond, Grand unification, in Grand Unified Theories and Related Topics, proceedings of the 4th Kyoto Summer Institute, World Scientific, Singapore, 1981.

  6. M. G. Barratt and S. Priddy, On the homology of non-connected monoids and their associated groups, Comm. Math. Helv. 47 (1972), 1-14.

week120

  1. Abhay Ashtekar and Kirill Krasnov, Quantum geometry and black holes, preprint available as arXiv:gr-qc/9804039.

  2. Kirill Krasnov, picture of a quantum black hole, http://math.ucr.edu/home/baez/blackhole.eps

  3. Louis Crane, David N. Yetter, On the classical limit of the balanced state sum, preprint available as arXiv:gr-qc/9712087.

  4. T. Regge, General relativity without coordinates, Nuovo Cimento 19 (1961), 558-571.

  5. David N. Yetter, Generalized Barrett-Crane vertices and invariants of embedded graphs, preprint available as arXiv:math.QA/9801131.

  6. John W. Barrett, The classical evaluation of relativistic spin networks, preprint available at arXiv:math.QA/9803063.

  7. Michael P. Reisenberger, Classical Euclidean general relativity from ``left-handed area = right-handed area'', preprint available as arXiv:gr-qc/9804061.

  8. Roberto De Pietri and Laurent Freidel, so(4) Plebanski action and relativistic spin foam model, preprint available as arXiv:gr-qc/9804071.

  9. Laurent Freidel and Kirill Krasnov, Discrete space-time volume for 3-dimensional BF theory and quantum gravity, preprint available as arXiv:hep-th/9804185.

  10. Ted Jacobson, Black hole thermodynamics today, to appear in Proceedings of the Eighth Marcel Grossmann Meeting, World Scientific, 1998, preprint available as arXiv:gr-qc/9801015.

  11. Rodolfo Gambini, Jorge Pullin, Does loop quantum gravity imply Lambda = 0?, preprint available as arXiv:gr-qc/9803097.

  12. R. Gambini, O. Obregon, and J. Pullin, Yang-Mills analogues of the Immirzi ambiguity, preprint available as arXiv:gr-qc/9801055.

  13. John Baez and Stephen Sawin, Diffeomorphism-invariant spin network states, to appear in Jour. Funct. Analysis, preprint available as arXiv:q-alg/9708005 or at http://math.ucr.edu/home/baez/int2.ps

  14. John H. Schwarz and Nathan Seiberg, String theory, supersymmetry, unification, and all that, to appear in the American Physical Society Centenary issue of Reviews of Modern Physics, March 1999, preprint available as arXiv:hep-th/9803179.

  15. Keith R. Dienes and Christopher Kolda, Twenty open questions in supersymmetric particle physics, 64 pages, preprint available as arXiv:hep-ph/9712322.

week121

  1. Marco Mackaay, Spherical 2-categories and 4-manifold invariants, available as math.QA/9805030

  2. John Baez and James Dolan, Categorification, to appear in the Proceedings of the Workshop on Higher Category Theory and Mathematical Physics at Northwestern University, Evanston, Illinois, March 1997, eds. Ezra Getzler and Mikhail Kapranov. Preprint available as arXiv:math.QA/9802029 or at http://math.ucr.edu/home/baez/cat.ps

  3. J. S. Carter and M. Saito, Knotted Surfaces and Their Diagrams, American Mathematical Society, Providence, 1998.

  4. Lawrence Breen, Braided n-categories and Sigma-structures, Prepublications Matematiques de l'Universite Paris 13, 98-06, January 1998, to appear in the Proceedings of the Workshop on Higher Category Theory and Mathematical Physics at Northwestern University, Evanston, Illinois, March 1997, eds. Ezra Getzler and Mikhail Kapranov.

  5. C. Balteanu, Z. Fiedorowicz, R. Schwaenzl, and R. Vogt, Iterated monoidal categories, available at arXiv:math.AT/9808082.

  6. Representation theory of Hopf categories, Martin Neuchl, Ph.D. dissertation, Department of Mathematics, University of Munich, 1997, available at http://www.mathematik.uni-muenchen.de/~neuchl

  7. Jim Stasheff, Grafting Boardman's cherry trees to quantum field theory, available as math.AT/9803156.

  8. Masoud Khalkhali, On cyclic homology of A_infinity algebras, available as arXiv:math.QA/9805051.

    Masoud Khalkhali, Homology of L_infinity algebras and cyclic homology, available as arXiv:math.QA/9805052.

week122

  1. Ivars Peterson, Loops of gravity: calculating a foamy quantum space-time, Science News, June 13, 1998, Vol. 153, No. 24, 376-377.

  2. Carlo Rovelli and Peush Upadhya, Loop quantum gravity and quanta of space: a primer, available as arXiv:gr-qc/9806079.

  3. Carlo Rovelli and Merced Montesinos, The fermionic contribution to the spectrum of the area operator in nonperturbative quantum gravity, available as arXiv:gr-qc/9806120.

  4. Carlo Rovelli, Strings, loops and others: a critical survey of the present approaches to quantum gravity. Plenary lecture on quantum gravity at the GR15 conference, Pune, India, available as arXiv:gr-qc/9803024.

  5. Renate Loll, Discrete approaches to quantum gravity in four dimensions, available as arXiv:gr-qc/9805049, also available as a webpage on Living Reviews in Relativity at http://relativity.livingreviews.org/Articles/lrr-1998-13/

  6. Living Reviews in Relativity, http://www.livingreviews.org

  7. J. Ambjorn, Quantum gravity represented as dynamical triangulations, Class. Quant. Grav. 12 (1995) 2079-2134.

  8. J. Ambjorn, M. Carfora, and A. Marzuoli, The Geometry of Dynamical Triangulations, Springer-Verlag, Berlin, 1998. Also available electronically as arXiv:hep-th/9612069 - watch out, this is 166 pages long!

  9. J. Ambjorn and R. Loll, Non-perturbative Lorentzian quantum gravity, causality and topology change, preprint available as arXiv:hep-th/9805108.

  10. Dirk Kreimer, Renormalization and knot theory, Journal of Knot Theory and its Ramifications, 6 (1997), 479-581. Preprint available as arXiv:q-alg/9607022 - beware, this is 103 pages long!

    Dirk Kreimer, On the Hopf algebra structure of perturbative quantum field theories, available as arXiv:q-alg/9707029.

  11. Thomas Krajewski and Raimar Wulkenhaar, On Kreimer's Hopf algebra structure of Feynman graphs, available as arXiv:hep-th/9805098.

week123

  1. Greg Egan, Axiomatic, Orion Books, 1995.

    Greg Egan, Luminous, Orion Books, 1998.

  2. Daniel C. Dennett and Douglas R. Hofstadter, The Mind's I: Fantasies and Reflections on Self and Soul, Bantam Books, 1982.

  3. Greg Egan, Closer, http://www.eidolon.net/old_site/issue_09/09_closr.htm

  4. Greg Egan, Foundations, http://www.netspace.net.au/~gregegan/FOUNDATIONS/index.html

  5. Gordon L. Kane, Experimental evidence for more dimensions reported, Physics Today, May 1998, 13-16.

    Paul M. Grant, Researchers find extraordinarily high temperature superconductivity in bio-inspired nanopolymer, Physics Today, May 1998, 17-19.

    Jack Watrous, Ribosomal robotics approaches critical experiments; government agencies watch with mixed interest, Physics Today, May 1998, 21-23.

  6. Laurent Freidel and Kirill Krasnov, Spin foam models and the classical action principle, available as arXiv:hep-th/9807092.

  7. Abhay Ashtekar, Alejandro Corichi and Jose A. Zapata, Quantum theory of geometry III: Non-commutativity of Riemannian structures, available as arXiv:gr-qc/9806041.

  8. Andre Hirschowitz, Carlos Simpson, Descente pour les n-champs (Descent for n-stacks), approximately 240 pages, in French, available as math.AG/9807049. arXiv:math.AG/9807049.

  9. Michael Batanin, Computads for finitary monads on globular sets, available at http://www-math.mpce.mq.edu.au/~mbatanin/papers.html

  10. Tom Leinster, Structures in higher-dimensional category theory, available at http://www.dpmms.cam.ac.uk/~leinster

  11. Alain Connes and Dirk Kreimer, Hopf algebras, renormalization and noncommutative geometry, available as arXiv:hep-th/9808042.

  12. Dirk Kreimer, How useful can knot and number theory be for loop calculations?, Talk given at the workshop "Loops and Legs in Gauge Theories", available as arXiv:hep-th/9807125.

  13. Jack Morava, Quantum generalized cohomology, available as arXiv:math.QA/9807058 and http://hopf.math.purdue.edu/

  14. Satyan L. Devadoss, Tessellations of moduli spaces and the mosaic operad, available as arXiv:math.QA/9807010.

week124

  1. Yuri I. Manin, Reflections on arithmetical physics, in Conformal Invariance and String Theory, eds. Petre Dita and Vladimir Georgescu, Academic Press, 1989.

  2. W. Wayt Gibbs, Monstrous moonshine is true, Scientific American, November 1998, 40-41. Also available at http://www.sciam.com/1998/1198issue/1198profile.html.

  3. Phillippe Di Francesco, Pierre Mathieu, and David Senechal, Conformal Field Theory, Springer, 1997.

  4. Victor Kac, Vertex Algebras for Beginners, American Mathematical Society, University Lecture Series vol. 10, 1997.

  5. Joseph Polchinski, String Theory, 2 volumes, Cambridge U. Press, 1998.

  6. E. Kiritsis, Introduction to Superstring Theory, 244 pages, to be published by Leuven University Press, available as arXiv:hep-th/9709062.

  7. Quantum Fields and Strings: A Course for Mathematicians, eds. P. Deligne, P. Etinghof, D. Freed, L. Jeffrey, D. Kazhdan, D. Morrison and E. Witten, American Mathematical Society, to appear.

  8. Abraham Pais, Maurice Jacob, David I. Olive, and Michael F. Atiyah, Review of Paul Dirac: The Man and His Work, Cambridge U. Press, 1998.

  9. Michael Berry, Paul Dirac: the purest soul in physics, Physics World, February 1998, pp. 36-40.

week125

  1. David Mumford, Picard groups of moduli problems, in Arithmetical Algebraic Geometry, ed. O. F. G. Schilling, Harper and Row, New York, 1965.

  2. Joe Harris and Ian Morrison, Moduli of Curves, Springer-Verlag, New York, 1998.

  3. K. Behrend, L. Fantechi, W. Fulton, L. Goettsche and A. Kresch, An Introduction to Stacks, in preparation.

  4. D. J. Broadhurst and D. Kreimer, Renormalization automated by Hopf algebra, available as arXiv:hep-th/9810087.

week126

  1. Michael B. Green, John H. Schwarz and Edward Witten, Superstring Theory, 2 volumes, Cambridge University Press.

  2. Neal Koblitz, Introduction to Elliptic Curves and Modular Forms, 2nd edition, Springer-Verlag, 1993.

  3. G. H. Hardy, Divergent Series, Chelsea Pub. Co., New York, 1991.

  4. Mathworld, Dedekind eta function, http://mathworld.wolfram.com/DedekindEtaFunction.html

  5. Wikipedia, Dedekind eta function, http://en.wikipedia.org/wiki/Dedekind_eta_function

week127

  1. Lennart Berggren, Jonathan Borwein and Peter Borwein, Pi: A Source Book, Springer-Verlag, New York, 1997.

  2. PiHex project, http://www.cecm.sfu.ca/projects/pihex/pihex.html

  3. Jean-Benoit Bost, Fibres determinants, determinants regularises, et mesures sur les espaces de modules des courbes complexes, Asterisque 152-153 (1987), 113-149.

  4. A. A. Beilinson and Y. I. Manin, The Mumford form and the Polyakov measure in string theory, Comm. Math. Phys. 107 (1986), 359-376.

  5. Charles Nash, Differential Topology and Quantum Field Theory, Academic Press, New York, 1991.

  6. A. M. Polyakov, Quantum geometry of bosonic strings, Phys. Lett. B103 (1981), 207.

  7. Richard E. Borcherds, What is moonshine?, talk given upon winning the Fields medal, preprint available as arXiv:math.QA/9809110.

  8. Peter Goddard, The work of R. E. Borcherds, preprint available as arXiv:math.QA/9808136.

  9. Cartoon by J. F. Cartier, http://www.physik.uni-frankfurt.de/~jr/gif/cartoon/cart 0785.gif

  10. R. T. Seeley, Complex powers of an elliptic operator, Proc. Symp. Pure Math. 10 (1967), 288-307.

week128

  1. John Archibald Wheeler and Kenneth Ford, Geons, Black Holes, and Quantum Foam: A Life in Physics, Norton, New York, 1998.

  2. Steven Carlip, Quantum Gravity in 2+1 Dimensions, Cambridge University Press, 1998. ISBN 0-521-56408-5.

  3. Jorge Pullin, editor, Matters of Gravity, vol. 12, available at arXiv:gr-qc/9809031 and at http://www.phys.lsu.edu//mog

  4. John W. Barrett, State sum models for quantum gravity, Penn State relativity seminar, August 27, 1998, audio and text of transparencies available at http://vishnu.nirvana.phys.psu.edu/online/Html/Seminars/Fall1998/Barrett/

  5. John W. Barrett and Ruth M. Williams, The asymptotics of an amplitude for the 4-simplex, preprint available as arXiv:gr-qc/9809032.

  6. Justin Roberts, Classical 6j-symbols and the tetrahedron, preprint available as math-ph/9812013.

  7. Andrea Barbieri, Space of the vertices of relativistic spin networks, preprint available as arXiv:gr-qc/9709076.

  8. Michael P. Reisenberger, On relativistic spin network vertices, preprint available as arXiv:gr-qc/9809067.

  9. Abhay Ashtekar, Chris Beetle and Steve Fairhurst, Mazatlan lectures on black holes, slides available at http://vishnu.nirvana.phys.psu.edu/online/Html/Conferences/Mazatlan/

  10. Abhay Ashtekar, Chris Beetle and S. Fairhurst, Isolated horizons: a generalization of black hole mechanics, preprint available as arXiv:gr-qc/9812065.

  11. Matthias Arnsdorf and R. S. Garcia, Existence of spinorial states in pure loop quantum gravity, preprint available as arXiv:gr-qc/9812006.

  12. Steve Carlip, Black hole entropy from conformal field theory in any dimension, preprint available as arXiv:hep-th/9812013.

week129

  1. Geometry and Quantum Physics lectures, 38th Internationale Universitaetswochen fuer Kern- und Teilchenphysik, http://physik.kfunigraz.ac.at/utp/iukt/iukt_99/iukt99-lect.html

  2. Geometry and Quantum Physics, proceedings of the 38th Int. Universitaetswochen fuer Kern- und Teilchenphysik, Schladming, Austria, Jan. 9-16, 1999, eds. H. Gausterer, H. Grosse and L. Pittner, to appear in Lecture Notes in Physics, Springer-Verlag, Berlin.

  3. Alain Connes, Noncommutative geometry and reality, J. Math. Phys. 36 (1995), 6194.

week130

  1. Special Report: Revolution in Cosmology, Scientific American, January 1999. Includes the articles "Surveying space-time with supernovae" by Craig J. Horgan, Robert P. Kirschner and Nicholoas B. Suntzeff, "Cosmological antigravity" by Lawrence M. Krauss, and "Inflation in a low-density universe" by Martin A. Bucher and David N. Spergel.

  2. Nikolas Solomey, The Elusive Neutrino, Scientific American Library, 1997.

  3. K. Grotz and H. V. Klapdor, The Weak Interaction in Nuclear, Particle and Astrophysics, Adam Hilger, Bristol, 1990.

  4. Klaus Winter, ed., Neutrino Physics, Cambridge U. Press, Cambridge, 1991.

  5. Felix Boehm and Petr Vogel, Physics of Massive Neutrinos, Cambridge U. Press, Cambridge, 1987.

  6. The neutrino oscillation industry, http://www.hep.anl.gov/NDK/hypertext/nu_industry.html

  7. Paul Langacker, Implications of neutrino mass, http://dept.physics.upenn.edu/neutrino/jhu/jhu.html

  8. Boris Kayser, Neutrino mass: where do we stand, and where are we going?, preprint available as arXiv:hep-ph/9810513.

  9. GALLEX collaboration, GALLEX solar neutrino observations: complete results for GALLEX II, Phys. Lett. B357 (1995), 237-247.

    Final results of the CR-51 neutrino source experiments in GALLEX, Phys. Lett. B420 (1998), 114-126.

    GALLEX solar neutrino observations: results for GALLEX IV, Phys. Lett. B447 (1999), 127-133.

  10. SAGE collaboration, Results from SAGE, Phys. Lett B328 (1994), 234-248.

    The Russian-American gallium experiment (SAGE) CR neutrino source measurement, Phys. Rev. Lett. 77 (1996), 4708-4711.

  11. LSND collaboration, Evidence for neutrino oscillations from muon decay at rest, Phys. Rev. C54 (1996) 2685-2708, preprint available as nucl-ex/9605001.

    Evidence for anti-muon-neutrino -> anti-electron-neutrino oscillations from the LSND experiment at LAMPF, Phys. Rev. Lett 77 (1996), 3082-3085, preprint available as nucl-ex/9605003.

    Evidence for muon-neutrino -> electron-neutrino oscillations from LSND, Phys. Rev. Lett. 81 (1998), 1774-1777, preprint available as nucl-ex/9709006.

    Results on muon-neutrino -> electron-neutrino oscillations from pion decay in flight, Phys. Rev. C58 (1998), 2489-2511.

  12. Super-Kamiokande collaboration, Evidence for oscillation of atmospheric neutrinos, Phys. Rev. Lett 81 (1998), 1562-1567, preprint available as arXiv:hep-ex/9807003.

  13. MACRO collaboration, Measurement of the atmospheric neutrino-induced upgoing muon flux, Phys. Lett. B434 (1998), 451-457, preprint available as arXiv:hep-ex/9807005.

  14. IMB collaboration, A search for muon-neutrino oscillations with the IMB detector, Phys. Rev. Lett 69 (1992), 1010-1013.

  15. V. Barger, T. J. Weiler, and K. Whisnant, Inferred 4.4 eV upper limits on the muon- and tau-neutrino masses, preprint available as arXiv:hep-ph/9808367.

  16. David O. Caldwell, The status of neutrino mass, preprint available as arXiv:hep-ph/9804367.

  17. Frank Wilczek, Beyond the Standard Model: this time for real, preprint available as arXiv:hep-ph/9809509.

  18. Lilian Hoddeson, Laurie Brown, Michael Riordan and Max Dresden, eds., The Rise of the Standard Model: Particle Physics in the 1960s and 1970s.

  19. LSU Super-Kamiokande group homepage, http://beavis.phys.lsu.edu/~superk/

week131

  1. Sheldon Lee Glashow, The new frontier, in First Workshop on Grand Unification, eds. Paul H. Frampton, Sheldon L. Glashow and Asim Yildiz, Math Sci Press, Brookline Massachusetts, 1980, pp. 3-8.

  2. Feza Gursey, Symmetry breaking patterns in E_6, in First Workshop on Grand Unification, eds. Paul H. Frampton, Sheldon L. Glashow and Asim Yildiz, Math Sci Press, Brookline Massachusetts, 1980, pp. 39-55.

  3. Greg Bothun, Modern Cosmological Observations and Problems, Taylor & Francis, London, 1998.

  4. Jayant V. Narlikar, Introduction to Cosmology, Cambridge U. Press, Cambridge, 1993.

  5. Peter Coles and Francesco Lucchin, Cosmology: The Origin and Evolution of Cosmic Structure, Wiley, New York, 1995.

  6. Sandip K. Chakrabarti, ed., Observational Evidence for Black Holes in the Universe, Kluwer, Dordrecht, 1998.

week132

  1. John Baez, Higher-dimensional algebra and Planck-scale physics, to appear in Physics Meets Philosophy at the Planck Scale, eds. Craig Callender and Nick Huggett, Cambridge U. Press. Preprint available as arXiv:gr-qc/9902017.

  2. Geraldine Brady and Todd H. Trimble. A string diagram calculus for predicate logic, and C. S. Peirce's system Beta, available at http://people.cs.uchicago.edu/~ brady

    Geraldine Brady and Todd H. Trimble, A categorical interpretation of Peirce's propositional logic Alpha, Jour. Pure and Appl. Alg. 149 (2000), 213-239.

    Geraldine Brady and Todd H. Trimble, The topology of relational calculus.

  3. J. Scott Carter, Louis H. Kauffman, and Masahico Saito, Structures and diagrammatics of four dimensional topological lattice field theories, to appear in Adv. Math., preprint available as arXiv:math.GT/9806023.

  4. J. Scott Carter, Daniel Jelsovsky, Selichi Kamada, Laurel Langford and Masahico Saito, Quandle cohomology and state-sum invariants of knotted curves and surfaces, preprint available as arXiv:math.GT/9903135.

  5. Tom Leinster, Structures in higher-dimensional category theory, preprint available at http://www.dpmms.cam.ac.uk/~leinster

  6. Claudio Hermida, Higher-dimensional multicategories, slides of a lecture given in 1997, available at http://www.math.mcgill.ca/~hermida

  7. Carlos Simpson, On the Breen-Baez-Dolan stabilization hypothesis for Tamsamani's weak n-categories, preprint available as arXiv:math.CT/9810058.

  8. Mark Hovey, Model Categories, American Mathematical Society Mathematical Surveys and Monographs, vol 63., Providence, Rhode Island, 1999.

  9. Frank Quinn, Group-categories, preprint available as arXiv:math.GT/9811047.

  10. Sjoerd Crans, A tensor product for Gray-categories, Theory and Applications of Categories, Vol. 5, 1999, No. 2, pp 12-69, available at http://www.tac.mta.ca/tac/volumes/1999/n2/abstract.html

week133

  1. Abhay Ashtekar, Quantum Mechanics of Geometry, preprint available as arXiv:gr-qc/9901023.

  2. Fotini Markopoulou, The internal description of a causal set: What the universe looks like from the inside, preprint available as arXiv:gr-qc/9811053.

    Fotini Markopoulou, Quantum causal histories, preprint available as arXiv:hep-th/9904009.

  3. Seth A. Major, Embedded graph invariants in Chern-Simons theory, preprint available as arXiv:hep-th/9810071.

  4. Lochlainn O'Raifeartaigh, Group structure of gauge theories, Cambridge University Press, Cambridge, 1986.

  5. Edward Witten, Search for a realistic Kaluza-Klein theory, Nucl. Phys. B186 (1981), 412-428.

    Edward Witten, Fermion quantum numbers in Kaluza-Klein theory, Shelter Island II, Proceedings: Quantum Field Theory and the Fundamental Problems of Physics, ed. T. Appelquist et al, MIT Press, 1985, pp. 227-277.

  6. Thomas Appelquist, Alan Chodos and Peter G. O. Freund, editors, Modern Kaluza-Klein Theories, Addison-Wesley, Menlo Park, California, 1987.

week134

  1. Minnowbrook Symposium on Space-Time Structure, program and transparencies of talks available at http://www.phy.syr.edu/research/he_theory/minnowbrook/#PROGRAM

  2. Carlo Rovelli, Quantum spacetime: what do we know?, to appear in Physics Meets Philosophy at the Planck Scale, eds. Craig Callender and Nick Huggett, Cambridge U. Press. Preprint available as arXiv:gr-qc/9903045.

  3. J. Butterfield and C. J. Isham, Spacetime and the philosophical challenge of quantum gravity, to appear in Physics Meets Philosophy at the Planck Scale, eds. Craig Callender and Nick Huggett, Cambridge U. Press. Preprint available as arXiv:gr-qc/9903072.

  4. John Baez and John Barrett, The quantum tetrahedron in 3 and 4 dimensions, preprint available as arXiv:gr-qc/9903060.

  5. Abhay Ashtekar, Alejandro Corichi and Kirill Krasnov, Isolated horizons: the classical phase space, preprint available as arXiv:gr-qc/9905089.

  6. Roberto De Pietri, Canonical "loop" quantum gravity and spin foam models, to appear in the proceedings of the XXIIIth Congress of the Italian Society for General Relativity and Gravitational Physics (SIGRAV), 1998, preprint available as arXiv:gr-qc/9903076.

  7. Seth Major, A spin network primer, to appear in Amer. Jour. Phys., preprint available as arXiv:gr-qc/9905020.

  8. Seth Major, Operators for quantized directions, preprint available as arXiv:gr-qc/9905019.

  9. John Baez, An introduction to spin foam models of BF theory and quantum gravity, in Geometry and Quantum Physics, eds. Helmut Gausterer and Harald Grosse, Lecture Notes in Physics, Springer-Verlag, Berlin, 2000, pp. 25-93. Preprint available as arXiv:gr-qc/9905087.

  10. John Barrett and Louis Crane, A Lorentzian signature model for quantum general relativity, preprint available as arXiv:gr-qc/9904025.

  11. Junichi Iwasaki, A surface theoretic model of quantum gravity, preprint available as arXiv:gr-qc/9903112.

  12. Richard E. Borcherds, Quantum vertex algebras, preprint available as arXiv:math.QA/9903038.

week135

  1. Toward a New Understanding of Space, Time and Matter, workshop home page at http://axion.physics.ubc.ca/Workshop/

  2. David W. Cohen, An Introduction to Hilbert Space and Quantum Logic, Springer-Verlag, New York, 1989.

  3. C. Piron, Foundations of Quantum Physics, W. A. Benjamin, Reading, Massachusetts, 1976.

  4. C. A. Hooker, editor, The Logico-algebraic Approach to Quantum Mechanics, two volumes, D. Reidel, Boston, 1975-1979.

  5. William Wooters and Wocjciech Zurek, A single quantum cannot be cloned, Nature 299 (1982), 802-803.

  6. Classical and Quantum Physics of Strong Gravitational Fields, program homepage with transparencies and audio files of talks at http://www.itp.ucsb.edu/~patrick/gravity99/

  7. LIGO project home page, http://www.ligo.caltech.edu/

  8. Other gravitational wave detection projects, http://www.ligo.caltech.edu/LIGO_web/other_gw/gw_projects.html

  9. Steve Carlip, Entropy from conformal field theory at Killing horizons, preprint available at arXiv:gr-qc/9906126.

  10. Abhay Ashtekar, Christopher Beetle, and Stephen Fairhurst, Mechanics of isolated horizons, preprint available as arXiv:gr-qc/9907068.

  11. Jerzy Lewandowski, Spacetimes admitting isolated horizons, preprint available as arXiv:gr-qc/9907058.

  12. John McKay, Semi-affine Coxeter-Dynkin graphs and $G \subseteq SU_2(C)$, preprint available as arXiv:math.QA/9907089.

  13. Igor Frenkel, Naihuan Jing and Weiqiang Wang, Vertex representations via finite groups and the McKay correspondence, preprint available as arXiv:math.QA/9907166.

    Quantum vertex representations via finite groups and the McKay correspondence, preprint available as arXiv:math.QA/9907175.

week136

  1. Category Theory 99 website, with abstracts of talks, http://www.mat.uc.pt/~ct99/

  2. School on Category Theory and Applications, Coimbra, July 13-17, 199, Textos de Matematica Serie B No. 21, Departamento De Matematica da Universidade de Coimbra. Contains: "n-Categories" by John Baez, "Algebraic theories" by M. Cristina Pedicchio, and "Chu Spaces: duality as a common foundation for computation and mathematics" by Vaughan Pratt.

  3. P. Gabriel and F. Ulmer, Lokal praesentierbare Kategorien, Springer Lecture Notes in Mathematics, Berlin, 1971.

  4. William Lawvere, Functorial Semantics of Algebraic Theories, Ph.D. Dissertation, University of Columbia, 1963. Summary appears under same title in: Proceedings of the National Academy of Sciences of the USA 50 (1963), 869-872.

  5. William Lawvere and Steve Schanuel, Conceptual Mathematics: A First Introduction to Categories, Cambridge U. Press, Cambridge, 1997.

  6. Jacques Penon, Approache polygraphique des $\infty$-categories non strictes, in Cahiers Top. Geom. Diff. 40 (1999), 31-79.

week137

  1. Michael Mueger, Galois theory for braided tensor categories and the modular closure, preprint available as arXiv:math.CT/9812040.

  2. John Baez, Higher-dimensional algebra II: 2-Hilbert spaces, Adv. Math. 127 (1997), 125-189. Also available as arXiv:q-alg/9609018.

  3. John Baez and James Dolan, Categorification, in Higher Category Theory, eds. Ezra Getzler and Mikhail Kapranov, Contemporary Mathematics vol. 230, AMS, Providence, 1998, pp. 1-36. Also available at arXiv:math.QA/9802029.

  4. A. Bruguieres, Categories premodulaires, modularisations et invariants des varietes de dimension 3, preprint.

  5. Stephen Sawin, Jones-Witten invariants for nonsimply-connected Lie groups and the geometry of the Weyl alcove, preprint available as arXiv:math.QA/9905010.

  6. Marco Mackaay, Finite groups, spherical 2-categories, and 4-manifold invariants, preprint available as arXiv:math.QA/9903003.

  7. Mikhail Khovanov, A categorification of the Jones polynomial, preprint available as arXiv:math.QA/9908171.

  8. J. Bernstein, Igor Frenkel and Mikhail Khovanov, A categorification of the Temperley-Lieb algebra and Schur quotients of U(sl_2) by projective and Zuckerman functors, to appear in Selecta Mathematica.

  9. Mikhail Khovanov, Graphical calculus, canonical bases and Kazhdan-Lusztig theory, Ph.D. thesis, Yale, 1997.

week138

  1. James Hartle and Stephen Hawking, Path integral derivation of black hole radiance, Phys. Rev. D13 (1976), 2188.

  2. James Hartle and Stephen Hawking, Wavefunction of the universe, Phys. Rev. D28 (1983), 2960.

week139

  1. Vipul Periwal, Cosmological and astrophysical tests of quantum gravity, preprint available at arXiv:astro-ph/9906253

  2. John Baez, Renormalization made easy, http://math.ucr.edu/home/baez/renormalization.html

  3. Herbert W. Hamber and Ruth M. Williams, Newtonian potential in quantum Regge gravity, Nucl. Phys. B435 (1995), 361-397.

  4. Steven Weinberg, Ultraviolet divergences in quantum theories of gravitation, in General Relativity: an Einstein Centenary Survey, eds. Stephen Hawking and Werner Israel, Cambridge U. Press, Cambridge (1979).

  5. Steven Weinberg, The cosmological constant problem, Rev. Mod. Phys. 61 (1989), 1.

  6. Claude Itzykson and Jean-Michel Drouffe, Statistical Field Theory, 2 volumes, Cambridge U. Press, 1989.

  7. Jean Zinn-Justin, Quantum Field Theory and Critical Phenomena, Oxford U. Press, Oxford, 1993.

  8. Jan Ambjorn, Bergfinnur Durhuus, and Thordur Jonsson, Quantum Geometry: A Statistical Field Theory Approach, Cambridge U. Press, Cambridge, 1997.

  9. Viqar Husain and Sebastian Jaimungal, Phase transition in quantum gravity, preprint available as arXiv:gr-qc/9908056.

week140

  1. Norman Macrae, John von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence and Much More, American Mathematical Society, Providence, Rhode Island, 1999.

  2. Steve Batterson, Stephen Smale: The Mathematician Who Broke the Dimension Barrier, American Mathematical Society, Providence, Rhode Island, 2000.

  3. Stephen Smale's web page, http://www.math.berkeley.edu/~smale/

  4. Roberto De Pietri, Laurent Freidel, Kirill Krasnov, and Carlo Rovelli, Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space, preprint available as arXiv:hep-th/9907154.

  5. Laurent Freidel, Kirill Krasnov and Raymond Puzio, BF description of higher-dimensional gravity, preprint available as arXiv:hep-th/9901069.

  6. Laurent Freidel and Kirill Krasnov, Simple spin networks as Feynman graphs, preprint available as arXiv:hep-th/9903192.

  7. John Barrett and Louis Crane, A Lorentzian signature model for quantum general relativity, preprint available as arXiv:gr-qc/9904025.

  8. Sameer Gupta, Causality in spin foam models, preprint available as arXiv:gr-qc/9908018.

  9. Matthias Arnsdorf and Sameer Gupta, Loop quantum gravity on non-compact spaces, preprint available as arXiv:gr-qc/9909053.

  10. Seth A. Major, Quasilocal energy for spin-net gravity, preprint available as arXiv:gr-qc/9906052.

  11. C. Di Bartolo, R. Gambini, J. Griego, J. Pullin, Consistent canonical quantization of general relativity in the space of Vassiliev knot invariants, preprint available as arXiv:gr-qc/9909063.

  12. John Baez, Spin foam perturbation theory, preprint available as arXiv:gr-qc/9910050 or at http://math.ucr.edu/home/baez/foam3.ps

week141

  1. Chris Mortensen, Inconsistent Mathematics, Kluwer, Dordrecht, 1995.

  2. John Milnor, Morse Theory, Princeton U. Press, Princeton, 1960.

  3. B. A. Dubrovin, A. T. Fomenko and S. P. Novikov, Modern Geometry - Methods and Applications, Part III: Introduction to Homology Theory, Springer-Verlag Graduate Texts, number 125, Springer, New York, 1990.

  4. John Milnor, On manifolds homeomorphic to the 7-sphere, Ann. Math 64 (1956), 399-405.

  5. M. Kervaire and J. Milnor, Groups of homotopy spheres I, Ann. Math. 77 (1963), 504-537.

  6. J. Levine, Lectures on groups of homotopy spheres, in Algebraic and Geometric Topology, Springer Lecture Notes in Mathematics number 1126, Springer, Berlin, 1985, pp. 62-95.

  7. Edward Witten, Global gravitational anomalies, Commun. Math. Phys. 100 (1985), 197-229.

  8. Detlef Gromoll and Wolfgang Meyer, An exotic sphere with nonnegative sectional curvature, Ann. Math. 100 (1974), 401-406.

  9. Frederick Wilhelm, An exotic sphere with positive curvature almost everywhere, preprint, May 12 1999.

  10. Nigel Hitchin, Harmonic spinors, Adv. Math. 14 (1974), 1-55.

  11. Reinhard Schultz, Circle actions on homotopy spheres bounding plumbing manifolds, Proc. A.M.S. 36 (1972), 297-300.

  12. Louis Kauffman, Knots and Physics, World Scientific, Singapore, 1991.

  13. Kristin Schleich and Donald Witt, Exotic spaces in quantum gravity, Class. Quant. Grav. 16 (1999) 2447-2469, preprint available as arXiv:gr-qc/9903086.

  14. Claire Voisin, Mirror Symmetry, American Mathematical Society, 1999.

  15. David A. Cox and Sheldon Katz, Mirror Symmetry and Algebraic Geometry, American Mathematical Society, Providence, Rhode Island, 1999.

  16. Shing-Tung Yau, editor, Mirror Symmetry I, American Mathematical Society, 1998.

    Brian Green and Shing-Tung Yau, editors, Mirror Symmetry II, American Mathematical Society, 1997.

    Duong H. Phong, Luc Vinet and Shing-Tung Yau, editors, Mirror Symmetry III, American Mathematical Society, 1999.

  17. P. Candelas, Lectures on complex manifolds, in Superstrings '87, eds. L. Alvarez-Gaume et al, World Scientific, Singapore, 1988, pp. 1-88.

  18. Robert E. Gompf and Andras I Stipsicz, 4-Manifolds and Kirby Calculus, Amderican Mathematical Society, 1999.

  19. C. T. C. Wall and A. A. Ranicki, Surgery on Compact Manifolds, 2nd edition, American Mathematical Society, 1999.

  20. Alexander A. Voronov, Homotopy Gerstenhaber algebras, preprint available as arXiv:math.QA/9908040.

  21. Maxim Kontsevich, Operads and motives in deformation quantization, Lett. Math. Phys. 48 (1999), 35-72, preprint available as arXiv:math.QA/9904055.

  22. James E. McClure and Jeffrey H. Smith, A solution of Deligne's conjecture, preprint available as arXiv:math.QA/9910126

week142

  1. John Baez, Subcellular life forms, http://math.ucr.edu/home/baez/subcellular.html

  2. GNU Go, http://www.gnu.org/software/gnugo/devel.html

  3. CGoban, http://www.inetarena.com/~wms/comp/cgoban/

  4. American Go Association, http://www.usgo.org/resources/

  5. The Nihon Kiin, Go: The World's Most Fascinating Game, 2 volumes, Sokosha Printing Co., Tokyo, 1973.

  6. Ishida Yoshio, Dictionary of Basic Joseki, 3 volumes, Ishi Press International, San Jose, California, 1977.

  7. Cho Chikun, All About Life and Death, 2 volumes, Ishi Press International, San Jose, California, 1993.

  8. Ishidea Yoshio, All About Thickness: Understanding Moyo and Influence, Ishi Press International, San Jose, California.

  9. Elwyn Berlekamp and David Wolfe, Mathematical Go: Chilling Gets the Last Point, A. K. Peters, Wellesley Massachusetts, 1994.

  10. Markus Enzenberger, The integration of a priori knowledge into a Go playing neural network, http://www.cgl.ucsf.edu/go/Programs/neurogo-html/NeuroGo.html

  11. Yasunari Kawabata, The Master of Go, trans. Edward G. Seidensticker, Knopf, New York, 1972.

  12. The I Ching or Book of Changes, trans. Richard Wilhelm and Cary F. Baynes, Princeton U. Press, Princeton, 1969.

    The Classic of Changes: A New Translation of the I Ching as Interpreted by Wang Bi, trans. Richard John Lynn, Columbia U. Press, 1994.

  13. Henri Darmon, A proof of the full Shimura-Taniyama-Weil conjecture is announced, Notices of the American Mathematical Society, 46 no. 11 (December 1999), 1397-1401.

  14. Mikhail Kapranov, Analogies between the Langlands correspondence and topological quantum field theory, in Functional Analysis on the Eve of the 21st Century, Vol. 1, Birkhaueser, Boston, pp. 119-151.

  15. M. Makkai, The multitopic omega-category of all multitopic omega-categories, preprint available at ftp://ftp.math.mcgill.ca/pub/makkai

week143

  1. Robrt F. Service, Does life's handedness come from within?, Science 286 (November 12, 1999), 1282-1283.

  2. Henri Poincare, The present and future of mathematical physics, Bull. Amer. Math. Soc. 12 (1906), 240-260. Reprinted as part of a retrospective issue of the Bull. of the Amer. Math. Soc., 37 (2000), 25-38, available at http://www.ams.org/bull/

  3. Carlo Rovelli, The century of the incomplete revolution: searching for general relativistic quantum field theory, to appear in the Journal of Mathematical Physics 2000 Special Issue, preprint available as arXiv:hep-th/9910131.

  4. LIGO homepage, http://www.ligo.caltech.edu/

  5. VIRGO homepage, http://www.pi.infn.it/virgo/

  6. GEO 600 homepage, http://www.geo600.uni-hannover.de/

  7. TAMA 300 homepage, http://tamago.mtk.nao.ac.jp/

  8. GRAVITON homepage, http://www.das.inpe.br/graviton/project.html

  9. European Space Agency's homepage on the LISA project, http://www.estec.esa.nl/spdwww/future/html/lisa.htm

    NASA's homepage on the LISA project: http://lisa.jpl.nasa.gov/

  10. Planck homepage, http://astro.estec.esa.nl/SA-general/Projects/Planck/planck.html

  11. Chandra homepage, http://chandra.harvard.edu/

  12. XMM homepage, http://sci.esa.int/xmm/

  13. MIT's Astro-E homepage, http://acis.mit.edu/syseng/astroe/xis_home.html

  14. Robert Irion, Space becomes a physics lab, Science 286 (1999), 2060-2062.

  15. Dark Matter Telescope homepage, http://dmtelescope.org

week144

  1. M. J. Freyberg and J. Trumper, eds., The Local Bubble and Beyond, proceedings of the IAU Colloquium no. 166, Springer Lecture Notes in Physics 506, Springer-Verlag, Berlin, 1998.

  2. Robert Irion, A crushing end for our galaxy, Science 287 (2000), 62-64.

  3. Roland Buser, The formation and early evolution of the Milky Way galaxy, Science 287 (2000), 69-74.

  4. Chandra resolves cosmic X-ray glow and finds mysterious new sources, press release available online at http://chandra.harvard.edu/press/00_releases/press_011400bg.html

  5. James Stasheff, Homotopy associativity of H-spaces I, Trans. Amer. Math. Soc. 108 (1963), 275-292.

    James Stasheff, Homotopy associativity of H-spaces II, Trans. Amer. Math. Soc. 108 (1963), 293-312.

  6. James Stasheff, H-spaces from a Homotopy Point of View, Springer Lecture Notes in Mathematics 161, Springer-Verlag, New York, 1970.

  7. Robert M. Dickau, Catalan numbers, http://forum.swarthmore.edu/advanced/robertd/catalan.html

  8. Kevin Brown, The meanings of Catalan numbers, http://www.seanet.com/~ksbrown/kmath322.htm

  9. Herbert Wilf, Generatingfunctionology, Academic Press, Boston, 1994. Also available for free at http://www.cis.upenn.edu/~wilf/

  10. Andre Joyal, Une theorie combinatoire des series formelles, Adv. Math. 42 (1981), 1-82.

  11. F. Bergeron, G. Labelle, and P. Leroux, Combinatorial species and tree-like structures, Cambridge, Cambridge U. Press, 1998.

  12. Richard P. Stanley, Enumerative Combinatorics, volume 2, Cambridge U. Press, Cambridge, 1999, pp. 219-229.

week145

  1. V. S. Varadarajan, Geometry of Quantum Mechanics, Springer-Verlag, Berlin, 2nd ed., 1985.

  2. Roger Mohr and Bill Trigs, Desargues' Theorem, http://spigot.anu.edu.au/people/samer/Research/Doc/ECV_Tut_Proj_Geom/node25.html

  3. Pappus' theorem (a JavaSketchPad demo by MathsNet), http://www.anglia.co.uk/education/mathsnet/dynamic/pappus.html

  4. Frederick W. Stevenson, Projective Planes, W. H. Freeman and Company, San Francisco, 1972.

  5. Marshall Hall, Projective Planes and Other Topics, California Institute of Technology, Pasadena, 1954.

  6. Marshall Hall, The Theory of Groups, Macmillan, New York, 1959.

  7. Robin Hartshorne, Foundations of Projective Geometry, Benjamin, New York, 1967.

  8. Daniel Pedoe, An Introduction to Projective Geometry, Macmillan, New York, 1963.

  9. A. Adrian Albert and Reuben Sandler, An Introduction to Finite Projective Planes, Holt, Rinehart and Winston, New York, 1968.

  10. Roger Mohr and Bill Triggs, Projective geometry for image analysis, http://spigot.anu.edu.au/people/samer/Research/Doc/ECV_Tut_Proj_Geom/node1.html

  11. J. M. Landsberg and L. Manivel: The projective geometry of Freudenthal's magic square, preprint available as arXiv:math.AG/9908039.

  12. Hans Freudenthal, Lie groups in the foundations of geometry, Adv. Math. 1 (1964) 143.

  13. Jacques Tits, Algebres alternatives, algebres de Jordan et algebres de Lie exceptionelles, Proc. Colloq. Utrecht, vol. 135, 1962.

  14. R. D. Schafer, Introduction to Non-associative Algebras, Academic Press, 1966.

  15. C. H. Barton and A. Sudbery, Magic squares of Lie algebras, preprint available as arXiv:math.RA/0001083.

week146

  1. Max Tegmark, Is the "theory of everything" merely the ultimate ensemble theory?, Ann. Phys. 270 (1998), 1-51, preprint available as arXiv:gr-qc/9704009.

    Max Tegmark, Which mathematical structure is isomorphic to the universe?, http://www.hep.upenn.edu/~max/toe.html

    Marcus Chown, Anything goes, New Scientist 158 (1998) 26-30, also available at http://www.hep.upenn.edu/~max/toe_press.html

  2. J. Ambjorn, J. Correia, C. Kristjansen, and R. Loll, On the relation between Euclidean and Lorentzian 2d quantum gravity, preprint avilable as arXiv:hep-th/9912267.

    J. Ambjorn, J. Jurkiewicz and R. Loll, Lorentzian and Euclidean quantum gravity - analytical and numerical results, preprint available as arXiv:hep-th/0001124.

    J. Ambjorn, J. Jurkiewicz and R. Loll, A non-perturbative Lorentzian path integral for gravity, preprint avilable as arXiv:hep-th/0002050.

  3. Abhay Ashtekar, Donald Marolf, Jose Mourao and Thomas Thiemann, Osterwalder-Schrader reconstruction and diffeomorphism invariance, preprint available as quant-ph/9904094.

  4. Abhay Ashtekar, Interface of general relativity, quantum physics and statistical mechanics: some recent developments, to appear in Annalen der Physik, preprint available as arXiv:gr-qc/9910101.

  5. Abhay Ashtekar, Alejandro Corichi, and Kirill Krasnov, Isolated horizons: the classical phase space, preprint available as arXiv:gr-qc/9905089.

    Abhay Ashtekar, Christopher Beetle, and Stephen Fairhurst, Mechanics of isolated horizons, Class. Quant. Grav. 17 (2000) 253-298, preprint available as arXiv:gr-qc/9907068.

    Abhay Ashtekar and Alejandro Corichi, Laws governing isolated horizons: inclusion of dilaton couplings, preprint available as arXiv:gr-qc/9910068.

    Jerzy Lewandowski, Space-times admitting isolated horizons, preprint available as arXiv:gr-qc/9907058.

  6. Michael Reisenberger and Carlo Rovelli, Spin foams as Feynman diagrams, preprint available as arXiv:gr-qc/0002083.

  7. Michael Reisenberger and Carlo Rovelli, Spacetime as a Feynman diagram: the connection formulation, preprint available as arXiv:gr-qc/0002095.

  8. Cayetano Di Bartolo, Rodolfo Gambini, Jorge Griego, and Jorge Pullin, Consistent canonical quantization of general relativity in the space of Vassiliev invariants, preprint available as arXiv:gr-qc/9909063.

    Canonical quantum gravity in the Vassiliev invariants arena: I. Kinematical structure, preprint available as arXiv:gr-qc/9911009.

    Canonical quantum gravity in the Vassiliev invariants arena: II. Constraints, habitats and consistency of the constraint algebra, preprint available as arXiv:gr-qc/9911010.

  9. Martin Bojowald, Loop Quantum Cosmology I: Kinematics, preprint available as arXiv:gr-qc/9910103.

    Martin Bojowald, Loop Quantum Cosmology II: Volume Operators, arXiv:gr-qc/9910104.

week147

  1. Mathematics: Frontiers and Perspectives, edited by Vladimir Arnold, Michael Atiyah, Peter Lax and Barry Mazur, AMS, Providence, Rhode Island, 2000.

  2. Mathematics Unlimited: 2001 and Beyond, edited by Bjorn Engquist and Wilfried Schmid, Springer Verlag, New York, 2000.

  3. The American Physical Society: A Century of Physics, available at http://timeline.aps.org/APS/home_HighRes.html

  4. John Baez and James Dolan, From finite sets to Feynman diagrams, preprint available as arXiv:math.QA/0004133

  5. James Propp and David Feldman, Producing new bijections from old, Adv. Math. 113 (1995), 1-44. Also available at http://www.math.wisc.edu/~propp/articles.html

  6. John Conway and Peter Doyle, Division by three. http://math.dartmouth.edu/~doyle/docs/three/three/three.html

  7. Daniel Loeb, Sets with a negative number of elements, Adv. Math. 91 (1992), 64-74.

  8. S. Schanuel, Negative sets have Euler characteristic and dimension, Lecture Notes in Mathematics 1488, Springer Verlag, Berlin, 1991, pp. 379-385.

  9. James Propp, Exponentiation and Euler measure, available as arXiv:math.CO/0204009.

  10. Andre Joyal, Regle des signes en algebre combinatoire, Comptes Rendus Mathmatiques de l'Academie des Sciences, La societe royale du Canada, VII (1985), 285-290.

  11. Matthias Blau and George Thompson, N = 2 topological gauge theory, the Euler characteristic of moduli spaces, and the Casson invariant, Comm. Math. Phys. 152 (1993), 41-71.

  12. Claudio Hermida, From coherent structures to universal properties, available at http://www.cs.math.ist.utl.pt/cs/s84/claudio.html

  13. K. A. Hardie, K. H. Kamps, R. W. Kieboom, A homotopy bigroupoid of a topological space, in: Categorical Methods in Algebra and Topology, pp. 209-222, Mathematik-Arbeitspapiere 48, Universitaet Bremen, 1997. Appl. Categ. Structures, to appear.

    K. A. Hardie, K. H. Kamps, R. W. Kieboom, A homotopy 2-groupoid of a Hausdorff space, preprint.

  14. William J. Floyd and Steven P. Plotnick, Growth functions on Fuchsian groups and the Euler characteristic, Invent. Math. 88 (1987), 1-29.

  15. R. I. Grigorchuk, Growth functions, rewriting systems and Euler characteristic, Mat. Zametki 58 (1995), 653-668, 798.

  16. John Baez, Euler characteristic versus homotopy cardinality, lecture at the Fields Institute Program on Applied Homotopy Theory, September 20, 2003. Available in PDF form at http://www.math.ucr.edu/home/baez/cardinality/

week148

  1. Clay Mathematics Institute, Millennium Prize Problems, http://www.claymath.org/prizeproblems/index.htm

  2. Abhay Ashtekar, John Baez and Kirill Krasnov, Quantum geometry of isolated horizons and black hole entropy, preprint available at arXiv:gr-qc/0005126 or at http://math.ucr.edu/home/baez/black2.ps

  3. John Wheeler, It from bit, in Sakharov Memorial Lecture on Physics, Volume 2, eds. L. Keldysh and V. Feinberg, Nova Science, New York, 1992.

  4. Abhay Ashtekar, Alejandro Corichi and Kirill Krasnov, Isolated horizons: the classical phase space, Advances in Theoretical and Mathematical Physics 3 (2000), 418-471. Preprint available at arXiv:gr-qc/9905089.

  5. Abhay Ashtekar, Chris Beetle and Steve Fairhurst, Mechanics of isolated horizons, Class. and Quant. Gravity 17 (2000), 253-298. Preprint available at arXiv:gr-qc/9907068.

  6. Stephen Smale, Mathematical problems for the next century, Mathematical Intelligencer, 20 (1998), 7-15. Also available in Postscript and PDF as item 104 on Smale's webpage, http://www.cityu.edu.hk/ma/staff/smale/bibliography.html

week149

  1. Graeme Segal, Elliptic cohomology, Asterisque 161-162 (1988), 187-201.

  2. Peter S. Landweber, editor, Elliptic Curves and Modular Forms in Algebraic Topology, Springer-Verlag Lecture Notes in Mathematics 1326, Springer, Berlin, 1988.

  3. Charles B. Thomas, Elliptic Cohomology, Kluwer, Dordrecht, 1999.

  4. Edward Witten, Elliptic genera and quantum field theory, Comm. Math. Phys. 109 (1987), 525-536.

  5. Friedrich Hirzebruch, Thomas Berger and Rainer Jung, Manifolds and Modular Forms, translated by Peter S. Landweber, Vieweg, Braunschweig (a publication of the Max Planck Institute for Mathematics in Bonn), 1992.

  6. J. Adams, Infinite Loop Spaces, Princeton U. Press, Princeton, 1978.

  7. J. Adams, Stable Homotopy and Generalized Homology, Chicago Lectures in Mathematics, U. Chicago Press, Chicago, 1974.

  8. J. P. May, The Geometry of Iterated Loop Spaces, Lecture Notes in Mathematics 271, Springer Verlag, Berlin, 1972.

  9. J. P. May, F. Quinn, N. Ray and J. Tornehave, Einfinity Ring Spaces and Einfinity Ring Spectra, Lecture Notes in Mathematics 577, Springer Verlag, Berlin, 1977.

  10. G. Carlsson and R. Milgram, Stable homotopy and iterated loop spaces, in Handbook of Algebraic Topology, ed. I. M. James, North-Holland, 1995.

  11. C. N. Yang, Magnetic monopoles, fiber bundles and gauge field, in Selected Papers, 1945--1980, with Commentary, W. H. Freeman and Company, San Francisco, 1983.

  12. Dusa McDuff, Configuration spaces of positive and negative particles, Topology 14 (1975), 91-107.

  13. Ross H. Street, The petit topos of globular sets, Macquarie Mathematics Report Number 98/232, March 1998.

  14. Ross H. Street and Michael Batanin, The universal property of the multitude of trees, Macquarie Mathematics Report Number 98/233, March 1998.

  15. Michael Batanin, Shuffle polytopes, cooperative games and 2-dimensional coherence for higher dimensional categories.

week150

  1. Lagrange points, http://map.gsfc.nasa.gov/html/lagrange.html

  2. Neil J. Cornish, The Lagrange points, available at http://www.astro.princeton.edu/~njc/lagrange.ps.gz

  3. Asteroid belt, http://www-groups.dcs.st-and.ac.uk/~history//Diagrams/Asteroids.gif

  4. Minor Planet Center, Trojan minor planets, http://cfa-www.harvard.edu/cfa/ps/lists/Trojans.html

  5. Paul Wiegert, Kimmo Innanen and Seppo Mikkola, Near-earth asteroid 3753 Cruithne - Earth's curious companion, http://www.astro.queensu.ca/~wiegert/

  6. Paul Schlyter, Hypothetical planets, http://seds.lpl.arizona.edu/nineplanets/nineplanets/hypo.html

  7. Astronomy picture of the day: Dione's Lagrange moon Helene, http://antwrp.gsfc.nasa.gov/apod/ap951010.html

  8. Bill Arnett, Introduction to the nine planets: Tethys, Telesto and Calypso, http://seds.lpl.arizona.edu/nineplanets/nineplanets/tethys.html

  9. SOHO website, http://sohowww.nascom.nasa.gov/

  10. MAP website, http://map.gsfc.nasa.gov/

  11. T. Uzer, Ernestine A. Lee, David Farrelly, and Andrea F. Brunello, Synthesis of a classical atom: wavepacket analogues of the Trojan asteroids, Contemp. Phys. 41 (2000), 1-14. Abstract available at http://www.catchword.co.uk/titles/tandf/00107514/v41n1/contp1-1.htm

  12. Dale Husemoller, Fibre Bundles, Springer-Verlag, New York, 1975.

  13. H. Blaine Lawson, Jr. and Marie-Louise Michelsohn, Spin Geometry, Princeton University Press, Princeton, 1989.

  14. Robert E. Stong, Notes on Cobordism Theory, Princeton University Press, Princeton, 1968.

  15. P. E. Conner and E. E. Floyd, The Relation of Cobordism to K-theories, Lecture Notes in Mathematics 28, Springer-Verlag, New York, 1966.

  16. Douglas C. Ravenel, Complex Cobordism and Stable Homotopy Groups of Spheres, Academic Press, 1986.

  17. Hirotaka Tamanoi, Elliptic Genera and Vertex Operator Super-Algebras, Springer Lecture Notes in Mathematics 1704, Springer, Berlin, 1999.

  18. Daniel Quillen, On the formal group laws of unoriented and complex cobordism theory, Bull. Amer. Math. Soc. 75 (1969), 1293-1298. Also available as http://projecteuclid.org/euclid.bams/1183530915

week151

  1. Colin Gough, Science and the Stradivarius, Physics World, vol. 13 no. 4, April 2000, 27-33.

  2. A. H. Benade, Fundamentals of Musical Acoustics, Oxford University Press, Oxford, 1976.

    L. Cremer, The Physics of the Violin, MIT Press, Cambridge, Massachusetts, 1984.

    N. H. Fletcher and T. D. Rossing, The Physics of Musical Instruments, 2nd edition, Springer, New York, 1998.

    C. Hutchins and V. Benade, editors, Research Papers on Violin Acoustics 1975-1993, 2 volumes, Acoustical Society of America, New York, 1997.

  3. Dusa McDuff, Configuration spaces of positive and negative particles, Topology 14 (1975), 91-107.

  4. Alan L. Carey, Diarmuid Crowley and Michael K. Murray, Principal bundles and the Dixmier-Douady class, Comm. Math. Physics 193 (1998) 171-196, also available as arXiv:hep-th/9702147.

  5. Pawel Gajer, Geometry of Deligne cohomology, Invent. Math. 127 (1997), 155-207, also available as alg-geom/9601025.

    Pawel Gajer, Higher holonomies, geometric loop groups and smooth Deligne cohomology, Advances in Geometry, Birkhauser, Boston, 1999, pp. 195-235.

  6. Jean-Luc Brylinski, Loop Spaces, Characteristic Classes and Geometric Quantization, Birkhauser, Boston, 1993. ISBN 0-176-3644-7

  7. Lawrence Breen, On the Classification of 2-Gerbes and 2-Stacks, Asterisque 225, 1994.

  8. Alan L. Carey and Michael K. Murray, Faddeev's anomaly and bundle gerbes, Lett. Math. Phys. 37 (1996), 29-36.

    Jouko Mickelsson, Gerbes and Hamiltonian quantization of chiral fermions, Lie Theory and Its Applications in Physics, World Scientific, Singapore, 1996, pp. 216-225.

    Michael K. Murray, Bundle gerbes, J. London Math. Soc. 54 (1996), 403-416.

    Alan L. Carey, Jouko Mickelsson and Michael K. Murray, Index theory, gerbes, and Hamiltonian quantization, Comm. Math. Phys. 183 (1997), 707-722, preprint available as hep-th/9511151.

    Alan L. Carey, Michael K. Murray and B. L. Wang, Higher bundle gerbes and cohomology classes in gauge theories, J. Geom. Phys. 21 (1997) 183-197, preprint available as hep-th/9511169.

    Alan L. Carey, Jouko Mickelsson and Michael K. Murray, Bundle gerbes applied to quantum field theory, Rev. Math. Phys. 12 (2000), 65-90, preprint available as hep-th/9711133.

week152

  1. Michael J. Crowe, A History of Vector Analysis, University of Notre Dame Press, Notre Dame, 1967.

  2. John Baez, Some thoughts on the number six, http://math.ucr.edu/home/baez/six.html

  3. Thomas L. Hankins, Sir William Rowan Hamilton, John Hopkins University Press, Baltimore, 1980.

  4. Robert Perceval Graves, Life of Sir William Rowan Hamilton, 3 volumes, Arno Press, New York 1975.

  5. W. R. Hamilton, Four and eight square theorems, Appendix 3 of vol. III of The Mathematical Papers of William Rowan Hamilton, eds. H. Halberstam and R. E. Ingram, Cambridge University Press, Cambridge, 1967.

  6. L. E. Dickson, On quaternions and their generalization and the history of the eight square theorem, Ann. Math. 20 (1919), 155-171.

  7. Heinz-Dieter Ebbinghaus et al, Numbers, Springer, New York, 1990.

week153

  1. Reviel Netz, The origins of mathematical physics: new light on an old question, Physics Today, June 2000, 32-37.

  2. The Walters Art Gallery, Archimedes Palimpsest website, http://www.thewalters.org/archimedes/frame.html

  3. Chris Rorres, Archimedes website, http://www.mcs.drexel.edu/~crorres/Archimedes/contents.html

  4. Raoul Bott, Lectures on K(X), Harvard University, Cambridge, 1963.

  5. Michael Atiyah, K-theory, W. A. Benjamin, New York, 1967.

  6. Max Karoubi, K-theory: an Introduction, Springer, Berlin, 1978.

  7. Graeme Segal, Elliptic cohomology, Asterisque 161-162 (1988), 187-201.

  8. Hirotaka Tamanoi, Elliptic Genera and Vertex Operator Super-Algebras, Springer Lecture Notes in Mathematics 1704, Springer, Berlin, 1999.

week154

  1. Hoi-Kwong Lo, Will quantum cryptography ever become a successful technology in the marketplace?, preprint available as quant-ph/9912011

  2. John Preskill, Lecture notes on quantum computation and quantum information theory, available at http://www.theory.caltech.edu/people/preskill/ph229

  3. Juan Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231-252, preprint available as arXiv:hep-th/9711200.

  4. Nathan Seiberg and Edward Witten, Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory, Nucl. Phys. B426 (1994) 19-52, preprint available as arXiv:hep-th/9407087.

  5. Edward Witten, String theory dynamics in various dimensions, Nucl. Phys. B443 (1995) 85-126, preprint available as arXiv:hep-th/9503124.

  6. Edward Witten, Anti-DeSitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253-291, preprint available as arXiv:hep-th/9802150.

  7. S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B428 (1998) 105-114, preprint available as arXiv:hep-th/9802109.

  8. Joseph Polchinski, Dirichlet branes and Ramond-Ramond charges, Phys. Rev. Lett. 75 (1995) 4724-4727, preprint available as arXiv:hep-th/9510017.

  9. Nathan Seiberg and Edward Witten, Monopoles, duality and chiral symmetry breaking in N=2 supersymmetric QCD, Nucl. Phys. B431 (1994) 484-550, preprint available as arXiv:hep-th/9408099.

  10. T. Banks, W. Fischler, S. H. Shenker, and L. Susskind, M-theory as a matrix model: a conjecture, Phys. Rev. D55 (1997), 5112-5128, preprint available as arXiv:hep-th/9610043.

  11. C. M. Hull and P. K. Townsend, Unity of superstring dualities, Nucl. Phys. B438 (1995) 109-137, preprint available as arXiv:hep-th/9410167.

  12. Edward Witten, Bound states of strings and p-branes, Nucl. Phys. B460 (1996), 335-350, preprint available as arXiv:hep-th/9510135.

  13. Searching top cited papers on SPIRES, at http://www.slac.stanford.edu/spires/hep/topcite.html

  14. P. Budinich and A. Trautman, The Spinorial Chessboard, Springer-Verlag, Berlin, 1988.

  15. Claude Chevalley, The Algebraic Theory of Spinors, Springer, Berlin, 1991.

  16. Eli Cartan, The Theory of Spinors, Dover Press, 1966.

  17. Pertti Lounesto, Clifford Algebras and Spinors, Cambridge U. Press, Cambridge, 1997.

  18. Dominic Joyce, Compact Manifolds with Special Holonomy, Oxford U. Press, Oxford, 2000.

  19. O. Aharony, S. S. Gubser, J. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183-386, preprint available as arXiv:hep-th/9905111.

  20. Clifford V. Johnson, D-brane primer, preprint available as arXiv:hep-th/0007170.

  21. G. Papadopoulos and P. K. Townsend, Compactification of D=11 supergravity on spaces of exceptional holonomy, preprint available as arXiv:hep-th/9506150.

  22. B. S. Acharya, N=1 heterotic-supergravity duality and Joyce manifolds, preprint available as arXiv:hep-th/9508046.

    N=1 heterotic/M-theory duality and Joyce manifolds, preprint available as arXiv:hep-th/9603033.

    N=1 M-theory-heterotic duality in three dimensions and Joyce manifolds, preprint available as arXiv:hep-th/9604133.

    Dirichlet Joyce manifolds, discrete torsion and duality, preprint available as arXiv:hep-th/9611036.

    M theory, Joyce orbifolds and super Yang-Mills, preprint available as arXiv:hep-th/9812205.

  23. Chien-Hao Liu, On the global structure of some natural fibrations of Joyce manifolds, preprint available as arXiv:hep-th/9809007.

week155

  1. Acme Klein bottles sliced in half, http://www.kleinbottle.com/sliced_klein_bottles.htm

  2. H. S. M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973.

    Regular Complex Polytopes, 2nd edition, Cambridge U. Press, Cambridge, 1991.

  3. Eric Weisstein, stella octangula, http://mathworld.wolfram.com/StellaOctangula.html

  4. Eric Weisstein, cube 5-compound, http://mathworld.wolfram.com/Cube5-Compound.html

  5. Eric Weisstein, tetrahedron 5-compound, http://mathworld.wolfram.com/Tetrahedron5-Compound.html

  6. Eric Weisstein, tetrahedron 10-compound, http://mathworld.wolfram.com/Tetrahedron10-Compound.html

  7. John Baez, Some thoughts on the number 6, http://math.ucr.edu/home/baez/six.html

  8. John Baez, Platonic solids in all dimensions, http://math.ucr.edu/home/baez/platonic.html

  9. Eric Weisstein, 24-cell, http://mathworld.wolfram.com/24-Cell.html

  10. Kevin Brown, Kepler's rhombic dodecahedron, http://www.seanet.com/~ksbrown/coinc2.htm

  11. Mark Newbold's rhombic dodecahedron page, http://dogfeathers.com/mark/rhdodec.html

  12. Eric Weisstein, 600-cell, http://mathworld.wolfram.com/600-Cell.html

  13. George W. Hart's Pavilion of Polyhedrality, http://www.georgehart.com/pavilion.html

  14. Victor Bulatov's Polyhedra Collection, http://www.physics.orst.edu/~bulatov/polyhedra/index.html

  15. Tony Smith, 24-cell animation, 120-cell, 600-cell, http://www.innerx.net/personal/tsmith/24anime.html

week156

  1. John Kormendy, Monsters at the heart of galaxy formation, Science 289 (2000), 1484-1485. Available online at http://www.sciencemag.org/cgi/content/full/289/5484/1484

  2. Laura Ferrarese and David Merritt, A fundamental relation between supermassive black holes and their host galaxies, Astrophys. J. Lett., 539, (2000) L9, preprint available as arXiv:astro-ph/0006053.

  3. Karl Gebhardt et al, A relationship between nuclear black hole mass and galaxy velocity dispersion, Astrophys. J. Lett. 539, (2000) L13, preprint available as arXiv:astro-ph/0006289.

  4. Supermassive Black Hole Group, Theory of black holes and galaxies, http://www.physics.rutgers.edu/~merritt/theory.htm

  5. Ed Colbert's homepage, http://www.pha.jhu.edu/~colbert/

    E. J. M. Colbert and R. F. Mushotzky, The nature of accreting black holes in nearby galaxy nuclei, preprint available as arXiv:astro-ph/9901023.

  6. A. Ptak, R. Griffiths, Hard X-ray variability in M82: evidence for a nascent AGN?, preprint available as arXiv:astro-ph/9903372.

  7. David Ceperley et al, Prospective superfluid molecular hydrogen, http://www.aip.org/physnews/graphics/html/h2.htm

  8. Slava Grebenev, Boris Sartakov, J. Peter Toennies, and Andrei F. Vilesov, Evidence for superfluidity in para-hydrogen clusters inside helium-4 droplets at 0.15 Kelvin, Science 5484 (2000), 1532-1535, available online at http://www.sciencemag.org/cgi/content/abstract/289/5484/1532

  9. R. F. Streater and A. S. Wightman, PCT, Spin and Statistics, and All That, Addison-Wesley, Reading, Massachusetts, 1989.

  10. CPLEAR homepage, http://cplear.web.cern.ch/cplear/Welcome.html

    CPLEAR collaboration, First direct observation of time-reversal non-invariance in the neutral kaon system, Phys. Lett. B 444 (1998) 43, available online with all other papers by this collaboration at http://cplear.web.cern.ch/cplear/cplear_pub.html

  11. Christina Hebert, Phyisicists find first direct evidence for tau neutrino at Fermilab, http://www.fnal.gov/directorate/public_affairs/story_neutrino/p1.html

  12. LEP shutdown postponed by one month, http://press.web.cern.ch/Press/Releases00/PR08.00ELEPRundelay.html

  13. Higgs Working Group webpage, http://fnth37.fnal.gov/higgs/higgs.html

  14. John Baez, Symplectic, quaternionic, fermionic, http://math.ucr.edu/home/baez/symplectic.html

week157

  1. Hermann Weyl, The Classical Groups, Their Invariants and Representations, Princeton U. Press, Princeton, 1997.

  2. Irene Verona Schensted, A Course on the Applications of Group Theory to Quantum Mechanics, NEO Press, Box 32, Peaks Island, Maine.

  3. Shlomo Sternberg, Group Theory and Physics, Cambridge U. Press, Cambridge, 1994.

  4. Gordon Douglas James and Adalbert Kerber, The Representation Theory of the Symmetric Group, Addison-Wesley, Reading, Massachusetts, 1981.

  6. Roe Goodman and Nolan R. Wallach, Representations and Invariants of the Classical Groups, Cambridge University Press, Cambridge, 1998.

  7. William Fulton, Young Tableaux: With Applications to Representation Theory and Geometry, Cambridge U. Press, Cambridge, 1997.

  8. William Fulton, Eigenvalues, invariant factors, highest weights, and Schubert calculus, Bull. Amer. Math. Soc. 37 (2000), 209-249, also available as arXiv:math.AG/9908012.

  9. Allen Knutson and Terence Tao, The honeycomb model of GL(n) tensor products I: the saturation conjecture, preprint available as arXiv:math.RT/9807160

  10. Allen Knutson, The symplectic and algebraic geometry of Horn's problem, preprint available as arXiv:math.LA/9911088.

  11. Allen Knutson and Terence Tao, Honeycombs and sums of Hermitian matrices, preprint available as arXiv:math.RT/0009048

week158

  1. The World in Eleven Dimensions: Supergravity, Supermembranes and M-theory, ed. M. J. Duff, Institute of Physics Publishing, Bristol, 1999.

  2. Edward Witten, Search for a realistic Kaluza-Klein theory, Nucl. Phys. B186 (1981), 412-428.

  3. Quantum Fields and Strings: A Course for Mathematicians, 2 volumes, eds. P. Deligne, P. Etinghof, D. Freed, L. Jeffrey, D. Kazhdan, D. Morrison and E. Witten, American Mathematical Society, Providence, Rhode Island, 1999.

  4. W. Nahm, Supersymmetries and their representations, Nucl. Phys. B135 (1978), 149-166.

  5. T. Kugo and P. Townsend, Supersymmetry and the division algebras, Nucl. Phys. B221 (1983), 357-380.

  6. G. Sierra, An application of the theories of Jordan algebras and Freudenthal triple systems to particles and strings, Class. Quant. Grav. 4 (1987) 227.

  7. J. M. Evans, Supersymmetric Yang-Mills theories and division algebras, Nucl. Phys. B298 (1988), 92.

  8. M. J. Duff, Supermembranes: the first fifteen weeks, Class. Quant. Grav. 5 (1988), 189-205.

  9. Feza Gursey and Chia-Hsiung Tze, On the Role of Division, Jordan, and Related Algebras in Particle Physics, World Scientific, Singapore, 1996.

  10. Jaak Lohmus, Eugene Paal and Leo Sorgsepp, Nonassociative Algebras in Physics, Hadronic Press, Palm Harbor, Florida, 1994.

week159

  1. Yi Ling and Lee Smolin, Eleven dimensional supergravity as a constrained topological field theory, available as arXiv:hep-th/0003285.

  2. M. J. Plebanski, On the separation of Einsteinian substructures, J. Math. Phys. 18 (1977), 2511.

  3. Pietro Fre, Comments on the six index photon in D = 11, preprint TH-3884-CERN.

  4. R. D'Auria and P. Fre, Geometric supergravity in D = 11 and its hidden supergroup, Nucl. Phys. B201 (1982), 101. Erratum, Nucl. Phys. B206 (182), 496.

  5. L. Castellani, P. Fre and P. van Nieuwenhuizen, A review of the group manifold approach and its applications to conformal supergravity, Ann. Phys. 136 (1981), 398.

  6. Martin Cederwall, Ulf Gran, Mikkel Nielsen, and Bengt Nillson, Generalised 11-dimensional supergravity, available as arXiv:hep-th/0010042.

week160

  1. Ralph D. Lorenz, The weather on Titan, Science 290 (October 20, 2000), 467-468.

    Caitlin A. Griffith, Joseph L. Hall and Thomas R. Geballe, Detection of daily clouds on Titan, Science 290 (October 20, 2000), 509-513.

  2. Richard A. Kerr, Neptune may crush methane into diamonds, Science 286 (October 1, 1999), 25.

    Laura Robin Benedetti, Jeffrey H. Nguyen, Wendell A. Caldwell, Hongjian Liu, Michael Kruger, and Raymond Jeanloz, Dissociation of CH4 at high pressures and temperatures: diamond formation in giant planet interiors?, Science 286 (October 1, 1999), 100-102.

  3. Science Magazine, http://www.sciencemag.org/search.dtl

  4. Alejandro Perez and Carlo Rovelli, A spin foam model without bubble divergences, available as arXiv:gr-qc/0006107.

  5. Alejandro Perez and Carlo Rovelli, Spin foam model for Lorentzian general relativity, available as arXiv:gr-qc/0009021.

  6. Alejandro Perez and Carlo Rovelli, 3+1 spinfoam model of quantum gravity with spacelike and timelike components, available as arXiv:gr-qc/0011037.

  7. Daniele Oriti and Ruth M. Williams, Gluing 4-simplices: a derivation of the Barrett-Crane spin foam model for Euclidean quantum gravity, available as arXiv:gr-qc/0010031.

  8. Carlo Rovelli, Notes for a brief history of quantum gravity, presented at the 9th Marcel Grossmann Meeting in Rome, July 2000. Available as arXiv:gr-qc/0006061.

week161

  1. Dava Sobel, Galileo's Daughter, Penguin Books, London, 2000.

  2. David B. Wilson, Kelvin and Stokes: A Comparative Study in Victorian Physics, Adam Hilger, Bristol, 1987.

  3. Don Howard and John Stachel eds., Einstein and the History of General Relativity, Birkhauser, Boston, 1989.

  4. John Baez, The end of the universe, http://math.ucr.edu/home/baez/end.html

  5. John D. Barrow and Frank J. Tipler, The Cosmological Anthropic Principle, Oxford U. Press, Oxford, 1988.

  6. John D. Barrow, The Book of Nothing, to be published.

  7. Bert Schroer, Facts and fictions about Anti de Sitter spacetimes with local quantum matter, available as arXiv:hep-th/9911100.

  8. Bert Schroer, Braided structure in 4-dimensional conformal quantum field theory, available as arXiv:hep-th/0012021.

week162

  1. The Universe Map, National Geographic Society, NSG #602011, 2000.

  2. Wil Tirion and Roger W. Sinnot, Sky Atlas 2000.0, 2nd edition, Cambridge U. Press, 1999.

  3. Lee Smolin, Three Roads to Quantum Gravity, Weidenfeld and Nicholson, 2000.

  4. Lynn E. Garner, An Outline of Projective Geometry, North Holland, New York, 1981.

  5. Ruth Moufang, Alternativkoerper und der Satz vom vollstaendigen Vierseit, Abhandlungen Math. Sem. Hamburg 9, (1933), 207-222.

  6. Pascual Jordan, Ueber eine Klasse nichtassociativer hyperkomplexer Algebren, Nachr. Ges. Wiss. Goettingen (1932), 569-575.

  7. Pascual Jordan, John von Neumann, Eugene Wigner, On an algebraic generalization of the quantum mechanical formalism, Ann. Math. 35 (1934), 29-64.

  8. G. Emch, Algebraic Methods in Statistical Mechanics and Quantum Field Theory, Wiley-Interscience, New York, 1972.

  9. Pascual Jordan, Ueber eine nicht-desarguessche ebene projektive Geometrie, Abhandlungen Math. Sem. Hamburg 16 (1949), 74-76.

  10. Murat Gunaydin and Feza Gursey, An octonionic representation of the Poincare group, Lett. Nuovo Cim. 6 (1973), 401-406.

  11. Murat Gunaydin and Feza Gursey, Quark structure and octonions, Jour. Math. Phys. 14 (1973), 1615-1667.

  12. Murat Gunaydin and Feza Gursey, Quark statistics and octonions, Phys. Rev. D9 (1974), 3387-3391.

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    Hans Freudenthal, Beziehungen der e7 und e8 zur Oktavenebene:

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    Jacques Tits, Le plan projectif des octaves et les groupes exceptionnels E6 et E7, Bull. Acad. Roy. Belg. Sci. 40 (1954), 29-40.

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week163

  1. Georges Ifrah, The Universal History of Numbers from Prehistory to the Invention of the Computer, Wiley, New York, 2000.

  2. Frequently asked questions about the MathWorld case, http://mathworld.wolfram.com/docs/faq.html

  3. Gordon and Breach et al v. AIP and APS, brief of amici curiae of the American Library Association, Association of Research Libraries and the Special Library Association, http://www.arl.org/scomm/gb/amici.html

  4. AIP/APS prevail in suit by Gordon and Breach, G&B to appeal, http://www.arl.org/newsltr/194/gb.html

  5. John Stilwell, The story of the 120-cell, AMS Notices 48 (January 2001), 17-24.

  6. Plato, Timaeus, translated by B. Jowett, in The Collected Dialogues, Princeton U. Press, Princeton, 1969 (see line 55c).

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week164

  1. Physics problems for the next millennium, http://feynman.physics.lsa.umich.edu/strings2000/millennium.html

  2. What questions have disappeared?, The World Question Center, http://www.edge.org/documents/questions/q2001.html

  3. Nobuo Shimada, Differentiable structures on the 15-sphere and Pontrjagin classes of certain manifolds, Nagoya Math. Jour. (12) 1957, 59-69.

  4. Jack Morava, Cobordism of symplectic manifolds and asymptotic expansions, a talk at the conference in honor of S.P. Novikov's 60th birthday, available as arXiv:math.SG/9908070.

  5. Detlev Buchholz, Current trends in axiomatic quantum field theory, available as arXiv:hep-th/9811233.

  6. Matt Visser, The reliability horizon, available as arXiv:gr-qc/9710020.

  7. Bianca Letizia Cerchiai and Julius Wess, q-Deformed Minkowski Space based on a q-Lorentz Algebra, available as arXiv:math.QA/9801104.

week165

  1. University of Wisconsin at Milwaukee, Center for Gravitation and Cosmology home page, http://www.gravity.phys.uwm.edu/

  2. Marcia Bartusiak, Einstein's Unfinished Symphony: Listening to the Sounds of Space-Time, Joseph Henry Press, Washington D.C., 2000.

  3. J. Friedman and R. Sorkin, Spin 1/2 from gravity, Phys. Rev. Lett 44 (1980), 1100.

  4. John Baez, The meaning of Einstein's equation, available at arXiv:gr-qc/0103044.

  5. John Baez, Toby Bartels and Miguel Carrion, Quantum Gravity Seminar, http://math.ucr.edu/home/baez/qg.html

  6. Craig Callender and Nick Huggett, eds., Physics Meets Philosophy at the Planck Scale: Contemporary Theories in Quantum Gravity, Cambridge U. Press, Cambridge, 2001.

  7. Martin Bojowald, Loop Quantum Cosmology I: Kinematics, Class. Quant. Grav. 17 (2000), 1489-1508, also available at arXiv:gr-qc/9919103

    Loop Quantum Cosmology II: Volume Operators, Class. Quant. Grav. 17 (2000), 1509-1526, also available at arXiv:gr-qc/9910104.

    Loop Quantum Cosmology III: Wheeler-DeWitt Operators, Class. Quant. Grav. 18 (2001), 1055-1070, also available at arXiv:gr-qc/0008052.

    Loop Quantum Cosmology IV: Discrete Time Evolution, Class. Quant. Grav. 18 (2001) 1071-1088, also available at arXiv:gr-qc/0008053.

    Absence of Singularity in Loop Quantum Cosmology, available at arXiv:gr-qc/0102069.

  8. Tom Leinster, General operads and multicategories, available as math.CT/9810053.

    Structures in higher-dimensional category theory, Ph.D. thesis, available at http://www.dpmms.cam.ac.uk/~leinster/shdctabs.html

    Up-to-homotopy monoids, available as arXiv:math.QA/9912084.

    Homotopy algebras for operads, available as math.QA/0002180. arXiv:math.QA/0002180.

    Operads in higher-dimensional category theory, available as arXiv:math.CT/0011106

  9. Eugenia Cheng, The relationship between the opetopic and multitopic approaches to weak n-categories, available at http://www.dpmms.cam.ac.uk/~elgc2/

    Equivalence between approaches to the theory of opetopes, available at http://www.dpmms.cam.ac.uk/~elgc2/

  10. Hermann Nicolai and Robert Helling, Supermembranes and M(atrix) theory, available as arXiv:hep-th/9809103.

  11. Washington Taylor, M(atrix) theory: matrix quantum mechanics as a fundamental theory, available as arXiv:hep-th/0101126.

week166

  1. Steven Finch, MathSoft Constants, http://pauillac.inria.fr/algo/bsolve/constant/constant.html

  2. The Mathematics Geneaology Project, http://hcoonce.math.mankato.msus.edu/

  3. John J. O'Connor and Edmund F. Robertson, The MacTutor History of Mathematics Archive, http://www-groups.dcs.st-andrews.ac.uk/~history/index.html

  4. Bernard Greenberg, The Mercator Projection, http://www.beanpaste.com/BSG/mercator.html

  5. Anthony M. Jacobi, Academic Family Tree, http://www.staff.uiuc.edu/%7Ea-jacobi/tree.html

  6. Robert L. Griess, Pieces of eight: semiselfdual lattices and a new foundation for the theory of Conway and Mathieu groups. Adv. Math. 148 (1999), 75-104.

  7. John H. Conway, Christopher S. Simons, 26 implies the Bimonster, Jour. Algebra 235 (2001), 805-814.

  8. Pierre Ramond, Boson-fermion confusion: the string path to supersymmetry, available at arXiv:hep-th/0102012.

  9. T. Pengpan and Pierre Ramond, M(ysterious) patterns in SO(9), Phys. Rep. 315 (1999) 137-152, also available as arXiv:hep-th/9808190.

week167

  1. Y. Jack Ng and H. van Dam, Measuring the foaminess of space-time with gravity-wave interferometers, Found. Phys. 30 (2000) 795-805, also available as arXiv:gr-qc/9906003

  2. Eugene P. Wigner, Relativistic invariance and quantum phenomena, Rev. Mod. Phys. 29 (1957), 255-268.

    H. Salecker and E. P. Wigner, Quantum limitations of the measurement of space-time distances, Phys. Rev. 109, (1958), 571-577. Also available at http://fangio.magnet.fsu.edu/~vlad/pr100/100yrs/html/chap14_toc.htm

  3. Ronald J. Adler, Ilya M. Nemenman, James M. Overduin, David I. Santiago, On the detectability of quantum spacetime foam with gravitational-wave interferometers, Phys. Lett. B477 (2000) 424-428, also available at arXiv:gr-qc/9909017.

  4. Y. Jack Ng and H. van Dam, On Wigner's clock and the detectability of spacetime foam with gravitational-wave interferometers, Phys. Lett. B477 (2000) 429-435, also available at arXiv:gr-qc/9911054.

  5. G. Amelino-Camelia, Quantum theory's last challenge, Nature 408 (2000) 661-664.

    Testable scenario for relativity with minimum length, available at arXiv:hep-th/0012238

  6. Ronald J. Adler and David I. Santiago, On gravity and the uncertainty principle, Mod. Phys. Lett. A14 (1999) 1371, also available at arXiv:gr-qc/9904026.

  7. J. Ellis, N.E. Mavromatos and D. V. Nanopoulos, Search for quantum gravity, Gen. Rel. Grav. 31 (1999) 1257-1262, also available as arXiv:gr-qc/9905048.

  8. Jorge Pullin and Rodolfo Gambini, Nonstandard optics from quantum spacetime, Phys. Rev. D59 (1999) 124021, also available as arXiv:gr-qc/9809038.

  9. J. Ellis, K. Farakos, N.E. Mavromatos, V. Mitsou and D.V. Nanopoulos, Astrophysical probes of the constancy of the velocity of light, Astrophys. J. 535 (2000) 139-151, also available as arXiv:astro-ph/9907340.

week168

  1. Martin Bojowald, Quantum Geometry and Symmetry, Shaker Verlag, Aachen, 2000. Available at http://www.shaker.de/Online-Gesamtkatalog/Details.asp?ISBN=3-8265-7741-8

  2. Martin Bojowald, The semiclassical limit of loop quantum cosmology, available at arXiv:gr-qc/0105113.

  3. Alejandro Perez, Finiteness of a spin foam model for euclidean quantum general relativity, Nucl. Phys. B599 (2001) 427-434. Also available at arXiv:gr-qc/0011058.

  4. John Baez and John W. Barrett, Integrability for relativistic spin networks, available at arXiv:gr-qc/0101107.

  5. Louis Crane, Alejandro Perez, Carlo Rovelli, A finiteness proof for the Lorentzian state sum spin foam model for quantum general relativity, available as arXiv:gr-qc/0104057.

  6. John Baez, The octonions, http://math.ucr.edu/home/baez/octonions/
    Also available at arXiv:math.RA/0105155.

week169

  1. Daniele Oriti, Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity, Rep. Prog. Phys. 64 (2001), 1489-1544. Also available at arXiv:gr-qc/0106091.

  2. Tom Leinster, Topology and higher-dimensional category theory: the rough idea, available at arXiv:math.CT/0106240.

  3. Markus Rost, On the dimension of a composition algebra, Documenta Mathematica 1 (1996), 209-214. Available at http://www.mathematik.uni-bielefeld.de/DMV-J/vol-01/10.html

  4. Dominik Boos, Ein tensorkategorieller Zugang zum Satz von Hurwitz (A tensor-categorical approach to Hurwitz's theorem), Diplomarbeit ETH Zurich, March 1998, available at http://www.mathematik.uni-bielefeld.de/~rost/data/boos.pdf

  5. John Baez, Topos theory in a nutshell, http://math.ucr.edu/home/baez/topos.html

  6. John Baez, Toby Bartels, and Miguel Carrion, Quantum gravity seminar, http://math.ucr.edu/home/baez/qg.html

week170

  1. Conference on Algebraic Topological Methods in Computer Science, Stanford University, http://math.stanford.edu/atmcs/index.htm

  2. Alejandro Perez, Finiteness of a spin foam model for euclidean quantum general relativity, Nucl. Phys. B599 (2001) 427-434. arXiv:gr-qc/0011058.

  3. John W. Barrett, The classical evaluation of relativistic spin networks, Adv. Theor. Math. Phys. 2 (1998), 593-600. Also available as arXiv:math.QA/9803063.

  4. John W. Barrett and Ruth M. Williams, The asymptotics of an amplitude for the 4-simplex, Adv. Theor. Math. Phys. 3 (1999), 209-215. Also available as arXiv:gr-qc/9809032.

  5. Noson S. Yanofsky, Obstructions to coherence: natural noncoherent associativity, Jour. Pure Appl. Alg. 147 (2000), 175-213. Also available at arXiv:math.QA/9804106.

    The syntax of coherence. To appear in Cahiers Top. Geom. Diff.. Also available at arXiv:math.CT/9910006.

    Coherence, homotopy and 2-theories. To appear in K-Theory. Also available at arXiv:math.CT/0007033.

  6. G. Maxwell Kelly and Ross Street, Review of the elements of 2-categories, Springer Lecture Notes in Mathematics 420, Berlin, 1974, pp. 75-103.

  7. Daniel G. Quillen, Homotopical Algebra, Springer Lecture Notes in Mathematics, vol. 43, Springer, Berlin, 1967.

  8. Mark Hovey, Model Categories, American Mathematical Society Mathematical Surveys and Monographs, vol 63., Providence, Rhode Island, 1999.

  9. Paul G. Goerss and John F. Jardine, Simplicial Homotopy Theory, Birkhauser, Boston, 1999.

week171

  1. Urban legends reference pages, The Prize's Rite, http://www.snopes2.com/science/nobel.htm

  2. Steve Carlip, Quantum gravity: a progress report, Rep. Prog. Phys. 64 (2001) 885-942, also available at arXiv:gr-qc/0108040.

  3. Ulf Daniellson, Introduction to string theory, Rep. Prog. Phys. 64 (2001) 51-96.

  4. Thomas Thiemann, Introduction to modern canonical quantum general relativity, 301 pages, available at arXiv:gr-qc/0110034.

  5. Rodolfo Gambini and Jorge Pullin, Consistent discretizations for classical and quantum general relativity, available as arXiv:gr-qc/0108062.

  6. Luca Bombelli, Statistical geometry of random weave states, available as arXiv:gr-qc/0101080.

  7. Michael Seifert, Angle and volume studies in quantized space, 85 pages, available as arXiv:gr-qc/0108047.

    Paul Chew, Voronoi/Delaunay Applet, http://www.cs.cornell.edu/Info/People/chew/Delaunay.html

week172

  1. Discrete Random Geometries and Quantum Gravity, http://www1.phys.uu.nl/Symposion/EUWorkshop.htm

  2. Wil McCarthy, Ultimate alchemy, Wired, October 2001, 150.

  3. Marc Kastner, Artificial atoms, Physics Today 46 (1993), 24. Also available at http://web.mit.edu/physics/people/marc_kastner.htm

  4. Leo Kouwenhoven and Charles Marcus, Quantum dots, Physics World, June 1998. Also available at http://marcuslab.harvard.edu/

  5. Terry Gannon, Monstrous moonshine and the classification of CFT, in Conformal Field Theory: New Non-Perturbative Methods in String and Field Theory, Yavuz Nutku, Cihan Saclioglu and Teoman Turgut, eds., Perseus Publishing, 2000.

  6. Sergeui N. Dorogovtsev and J.F.F. Mendes, Evolving networks, available at cond-mat/0106144.

  7. John Baez and J. Daniel Christensen, Positivity of spin foam amplitudes, available at arXiv:gr-qc/0110044.

  8. J. Daniel Christensen and Greg Egan, An efficient algorithm for the Riemannian 10j symbols, available at arXiv:gr-qc/0110045.

  9. N. Ishibashi, H. Kawai, Y. Kitazawa and T. Tsuchiya, A large-N reduced model as superstring, Nucl. Phys. B498 (1997) 467-491. Also available as arXiv:hep-th/9612115.

  10. Peter Austing and John F. Wheater, Convergent Yang-Mills matrix theories, JHEP 0104 (2001) 019. Also available as arXiv:hep-th/0103159.

  11. Z. Burda, B. Petersson, J. Tabaczek, Geometry of reduced supersymmetric 4D Yang-Mills integrals, Nucl. Phys. B602 (2001) 399-409. Also available as arXiv:hep-lat/0012001.

  12. A. Konechny and A. Schwarz, Introduction to M(atrix) theory and noncommutative geometry, available at arXiv:hep-th/0012145.

  13. A. J. Wilkie, On exponentiation - a solution to Tarski's high school algebra problem, to appear in Quaderni di Matematica. Also available at http://www.maths.ox.ac.uk/~wilkie/

  14. R. Gurevic, Equational theory of positive numbers with exponentiation, Proc. Amer. Math. Soc. 94 (1985), 135-141.

  15. Marcel G. Jackson, A note on HSI-algebras and counterexamples to Wilkie's identity, Algebra Universalis 36 (1996), 528-535. Also available at http://www.latrobe.edu.au/mathstats/Staff/Marcel/details/publications.html

  16. R. Gurevic, Equational theory of positive numbers with exponentiation is not finitely axiomatizable, Ann. Pure. Appl. Logic 49 (1990), 1-30.

week173

  1. Favorite Leonid images found posted on the net, http://leonids.arc.nasa.gov/image_favorites.html

  2. Thomas Püttmann and A. Rigas, Isometric actions on the projective planes and embedded generators of homotopy groups. Available at http://www.ruhr-uni-bochum.de/mathematik8/puttmann/index.html.

  3. Matteo Mainetti and Catherine Huafei Yan, Arguesian identities in linear lattices, Adv. Math. 144 (1999), 50-93.

  4. Mark Haiman, Proof theory for linear lattices, Adv. Math. 58 (1985), 209-242.

  5. D. Finberg, M. Mainetti and G.-C. Rota, The logic of commuting equivalence relations, in Logic and Algebra, eds. A. Ursini and P. Agliano, Lecture Notes in Pure and Applied Mathematics, vol. 180, Decker, New York 1996.

  6. Michael Mueger, Conformal field theory and Doplicher-Roberts reconstruction, available at math-ph/0008027.

    From subfactors to categories and topology I: Frobenius algebras in and Morita equivalence of tensor categories, available at arXiv:math.CT/0111204.

    From subfactors to categories and topology II: The quantum double of tensor catgories and subfactors, available at arXiv:math.CT/0111205.

week174

  1. Thomas Hawkins, The Emergence of the Theory of Lie Groups: an Essay in the History of Mathematics, 1869-1926, Springer, New York, 2000.

  2. Michael Mueger, From subfactors to categories and topology I: Frobenius algebras in and Morita equivalence of tensor categories, available at arXiv:math.CT/0111204.

  3. Stephen Schanuel and Ross Street, The free adjunction, Cah. Top. Geom. Diff. 27 (1986), 81-83.

  4. Frank Quinn, Lectures on axiomatic quantum field theory, in Geometry and Quantum Field Theory, Amer. Math. Soc., Providence, RI, 1995.

  5. Lowell Abrams, Two-dimensional topological quantum field theories and Frobenius algebras, J. Knot Theory and its Ramifications 5 (1996), 569-587.

  6. L. Kadison, New Examples of Frobenius Extensions, University Lecture Series #14, Amer. Math. Soc., Providence RI, 1999.

week175

  1. Dava Sobel, Longitude, Fourth Estate Ltd., London, 1996.

  2. E. G. Richards, Mapping Time: The Calendar and its History, Oxford U. Press, Oxford, 1998.

  3. John Baez, The wobbling of the earth and other curiosities, http://math.ucr.edu/home/baez/wobble.html

  4. Alain Connes, Andre Lichnerowicz and Marcel Paul Schutzenberger, A Triangle of Thoughts, AMS, Providence, 2000.

  5. Masamichi Takesaki, Theory of Operator Algebras I, Springer, Berlin, 1979.

  6. Richard V. Kadison and John Ringrose, Fundamentals of the Theory of Operator Algebras, 4 volumes, Academic Press, New York, 1983-1992.

  7. Shoichiro Sakai, C*-algebras and W*-algebras, Springer, Berlin, 1971.

  8. Gerard G. Emch, Algebraic Methods in Statistical Mechanics and Quantum Field Theory, Wiley-Interscience, New York, 1972.

  9. Rudolf Haag, Local Quantum Physics: Fields, Particles, Algebras, Springer, Berlin, 1992.

  10. Ola Bratelli and Derek W. Robinson, Operator Algebras and Quantum Statistical Mechanics, 2 volumes, Springer, Berlin, 1987-1997.

week176

  1. Jan T. Kleyna, Mark I. Wilkinson, N. Wyn Evans and Gerard Gilmore, First clear signature of an extended dark matter halo in the Draco dwarf spheroidal, Astrophysical Journal Letters 563 (2001), L115-118. Also available at arXiv:astro-ph/0111329.

  2. UK Dark Matter Collaboration (UKDMC) homepage, http://hepwww.rl.ac.uk//UKDMC/

  3. DAMA collaboration, Searching for the WIMP annual signature by the ~100 kg NaI(Tl) set-up, http://www.lngs.infn.it/lngs/htexts/dama/dama39.html

  4. Dark Matter (DAMA) experiment home page, http://www.lngs.infn.it/lngs/htexts/dama/welcome.html

  5. Cryogenic Dark Matter Search (CDMS) home page, http://cdms.berkeley.edu/

  6. Frederic Mayet, Dark Matter Portal, http://isnwww.in2p3.fr/ams/fred/dm.html

  7. Edward R. Harrison, Cosmology, the Science of the Universe, Cambridge University Press, Cambridge, 1981.

  8. M. Berry, Cosmology and Gravitation, Adam Hilger, Bristol, 1986.

  9. John A. Peacock, Cosmological Physics, Cambridge University Press, Cambridge, 1999.

  10. Shaaban Khalil and Carlos Munoz, The enigma of the dark matter, to appear in Contemp. Phys., also available at arXiv:hep-ph/0110122.

  11. Leszek Roszkowski, Non-baryonic dark matter, available as arXiv:hep-ph/0102327.

  12. B. J. Carr, Recent developments in the search for baryonic dark matter, available as arXiv:astro-ph/0102389.

  13. V. C. de Andrade, L. C. T. Guillen and J. G. Pereira, Teleparallel gravity: an overview, available at arXiv:gr-qc/0011087.

  14. Yakov Itin, Energy-momentum current for coframe gravity, available as arXiv:gr-qc/0111036.

  15. >From subfactors to categories and topology I: Frobenius algebras in and Morita equivalence of tensor categories, available as arXiv:math.CT/0111204.

  16. Michael Mueger, On the structure of modular categories, available as arXiv:math.CT/0201017.

week177

  1. Greg Egan, Schild's Ladder, Eos, May 2002. Synopsis available at http://www.netspace.net.au/~gregegan/SCHILD/SCHILD.html

  2. Abhay Ashtekar, Quantum geometry and gravity: recent advances, available as arXiv:gr-qc/0112038.

    Abhay Ashtekar, Quantum geometry in action: big bang and black holes, available as math-ph/0202008.

  3. Aleksandar Mikovic, Spin foam models of matter coupled to gravity, arXiv:hep-th/0108099.

    Aleksandar Mikovic, Quantum field theory of open spin networks and new spin foam models, available as arXiv:gr-qc/0202026.

  4. Matthias Arnsdorf, Relating covariant and canonical approaches to triangulated models of quantum gravity, available as arXiv:gr-qc/0110026.

  5. Rodolfo Gambini and Jorge Pullin, A finite spin-foam-based theory of three and four dimensional quantum gravity, arXiv:gr-qc/0111089.

  6. Robert Oeckl, Generalized lattice gauge theory, spin foams and state sum invariants, available as arXiv:hep-th/0110259.

    Florian Girelli, Robert Oeckl and Alejandro Perez, Spin foam diagrammatics and topological invariance, available as arXiv:gr-qc/0111022.

  7. John C. Baez, J. Daniel Christensen, Thomas R. Halford and David C. Tsang, Spin foam models of Riemannian quantum gravity, arXiv:gr-qc/0202017.

  8. Roberto De Pietri, Laurent Freidel, Kirill Krasnov, and Carlo Rovelli, Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space, preprint available as arXiv:hep-th/9907154.

  9. Alejandro Perez and Carlo Rovelli, A spin foam model without bubble divergences, Nucl. Phys. B599 (2001), 255-282. Also available as arXiv:gr-qc/0006107.

    Alejandro Perez, Finiteness of a spin foam model for Euclidean quantum general relativity, Nucl. Phys. B599 (2001), 427-434. Also available as arXiv:gr-qc/0011058.

    Alejandro Perez, Group quantum field theories and spin foam models for quantum gravity, to appear.

week178

  1. J. Peter May, Operadic categories, Ainfinity categories and n-categories, writeup of a talk given in Morelia, Mexico, May 25, 2001. Available with other papers at his homepage, http://www.math.uchicago.edu/~may/

  2. Tom Leinster, A survey of definitions of n-category, available at arXiv:math.CT/0107188.

  3. Carlos Simpson, Some properties of the theory of n-categories, available at math.CT/0110273. arXiv:math.CT/0110273.

  4. Martin Markl, Steve Shnider and Jim Stasheff, Operads in Algebra, Topology and Physics, AMS, Providence, 2002.

  5. F. Morel, Voevodsky's proof of Milnor's conjecture, Bull. Amer. Math. Soc. 35 (1998), 123-143. Also available at http://e-math.ams.org/jourcgi/amsjournal?fn=120&pg1=pii&s1=S0273097998007459

  6. Hans Freudenthal, Lie groups in the foundations of geometry, Adv. Math. 1 (1964), 145-190.

  7. Hans Freudenthal and H. de Vries, Linear Lie groups, Academic Press, New York, 1969.

  8. William Fulton and Joe Harris, Representation Theory - a First Course, Springer Verlag, Berlin, 1991.

  9. Robert J. Baston and Michael G. Eastwood, The Penrose Transform: its Interaction with Representation Theory, Clarendon Press, Oxford,

week179

  1. Alain Connes and Dirk Kreimer, Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and main theorem, Comm. Math. Phys. 210 (2000), 249-273. Also available as arXiv:hep-th/9912092.

  2. G. Scharf, Finite Quantum Electrodynamics, Springer, Berlin, 1995.

  3. Alain Connes and Dirk Kreimer, Renormalization in quantum field theory and the Riemann-Hilbert problem I: the beta-function, diffeomorphisms and the renormalization group, Comm. Math. Phys. 216 (2001), 215-241. Also available as arXiv:hep-th/0003188.

  4. Dirk Kreimer, Knots and Feynman Diagrams, Cambridge University Press, Cambridge, 2000.

  5. Andrew Pressley and Graeme Segal, Loop Groups, Oxford University Press, Oxford, 1986.

  6. David Berenstein, Juan Maldacena and Horatiu Nastase, Strings in flat space and pp waves from N = 4 Super Yang Mills, available as arXiv:hep-th/0202021.

  7. Yuri Manin and Matilde Marcolli, Holography principle and arithmetic of algebraic curves, available as arXiv:hep-th/0201036.

week180

  1. Cosmic X-rays reveal evidence for new form of matter, http://www1.msfc.nasa.gov/NEWSROOM/news/releases/2002/02-082.html

  2. Peter Johnstone, Sketches of an Elephant: a Topos Theory Compendium, Cambridge U. Press. Volume 1, comprising Part A: Toposes as Categories, and Part B: 2-categorical Aspects of Topos Theory, 720 pages, to appear in June 2002. Volume 2, comprising Part C: Toposes as Spaces, and Part D: Toposes as Theories, 880 pages, to appear in June 2002. Volume 3, comprising Part E: Homotopy and Cohomology, and Part F: Toposes as Mathematical Universes, in preparation.

  3. John Baez, Topos theory in a nutshell, http://math.ucr.edu/home/baez/topos.html

  4. Colin McLarty, Elementary Categories, Elementary Toposes, Oxford University Press, Oxford, 1992.

  5. William Fulton and Joe Harris, Representation Theory - a First Course, Springer Verlag, Berlin, 1991.

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    Cristopher Moore, The 3-body (and n-body) problem, http://www.santafe.edu/~moore/gallery.html

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  4. Ronald L. Graham, Donald E. Knuth, and Oren Patashnik, Concrete Mathematics: a Foundation for Computer Science, 2nd edition, Addison-Wesley, Reading, Massachusetts, 1994.

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  4. Paul Garrett, Buildings and Classical Groups, Chapman & Hall, London, 1997.

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  3. Curt Cutler and Kip Thorne, An overview of gravitational-wave sources, available as arXiv:gr-qc/0204090.

  4. First lock at LIGO Hanford Observatory, http://www.ligo.caltech.edu/LIGO_web/firstlock/

  5. Washington quake rattles Hanford Observatory, http://www.ligo.caltech.edu/LIGO_web/news/0228quake.html

  6. LIGO's first science run: a special report, http://www.ligo.caltech.edu/LIGO_web/0209news/0209s1r1.html

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    Both also available at http://math.ucr.edu/home/baez/area.html

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    II, The chiral measure on moduli space, Nucl. Phys. B636 (2002), 3-60. Also available as arXiv:hep-th/0110283.

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    IV, The cosmological constant and modular forms, Nucl. Phys. B639 (2002), 129-181. Also available as arXiv:hep-th/0111040.

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  4. Ned Wright's Cosmology Tutorial, http://www.astro.ucla.edu/~wright/cosmolog.htm

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  3. Stephan Stolz and Peter Teichner, What is an elliptic object? http://math.ucsd.edu/~teichner/Preprints/Oxford.pdf

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  16. F. William Lawvere, Categorical dynamics, in Proceedings of Aarhus May 1978 Open House on Topos Theoretic Methods in Geometry, Aarhus/Denmark (1979).

  17. F. William Lawvere, Toward the description in a smooth topos of the dynamically possible motions and deformations of a continuous body, Cahiers de Topologie et Geometrie Differentielle Categorique 21 (1980), 337-392.

  18. Anders Kock, Synthetic Differential Geometry, Cambridge U. Press, Cambridge, 1981.

  19. F. William Lawvere and S. Schanuel, editors, Categories in Continuum Physics, Springer Lecture Notes in Mathematics No. 1174, Springer, Berlin, 1986.

  20. F. William Lawvere, Foundations and applications: axiomatization and education, Bulletin of Symbolic Logic 9 (2003), 213-224. Also available at http://www.math.ucla.edu/~asl/bsl/0902/0902-006.ps

  21. Colin McLarty, Elementary Categories, Elementary Toposes, Clarendon Press, Oxford, 1995.

  22. R. Blackwell, G. M. Kelly, and A. J. Power, Two-dimensional monad theory, Jour. Pure Appl. Algebra 59 (1989), 1-41.

  23. Brian Day and Ross Street, Monoidal bicategories and Hopf algebroids, Adv. Math. 129 (1997) 99-157.

  24. F. Marmolejo, Doctrines whose structure forms a fully faithful adjoint string, Theory and Applications of Categories 3 (1997), 23-44. Available at http://www.tac.mta.ca/tac/volumes/1997/n2/3-02abs.html

  25. S. Lack, A coherent approach to pseudomonads, Adv. Math. 152 (2000), 179-202. Also available at http://www.maths.usyd.edu.au:8000/u/stevel/papers/psm.ps.gz

  26. Peter Johnstone, Sketches of an Elephant: a Topos Theory Compendium, Oxford U. Press, Oxford. Volume 1, comprising Part A: Toposes as Categories, and Part B: 2-categorical Aspects of Topos Theory, 720 pages, 2002. Volume 2, comprising Part C: Toposes as Spaces, and Part D: Toposes as Theories, 880 pages, 2002.

  27. F. William Lawvere, Functorial Semantics of Algebraic Theories and Some Algebraic Problems in the context of Functorial Semantics of Algebraic Theories, reprints in Theory and Applications of Categories, 5 (2004) 1-121. Available at http://www.tac.mta.ca/tac/reprints/articles/5/tr5abs.html

week201

  1. Ian Stewart, Galois Theory, 3rd edition, Chapman and Hall, New York, 2004.

  2. H. P. F. Swinnerton-Dyer, A Brief Guide to Algebraic Number Theory, Cambridge U. Press, Cambridge 2001.

  3. Juergen Neukirch, Algebraic Number Theory, trans. Norbert Schappacher, Springer, Berlin, 1986.

  4. K. Iwasawa, On solvable extensions of algebraic number fields, Ann. Math. 58 (1953) 548-572.

  5. Pierre Deligne, Le groupe fondamental de la droite projective moins trois points, in Galois Groups over Q, MSRI Publications 16 (1989), 79-313.

  6. Leila Schneps, The Grothendieck-Teichmueller group: a survey, in The Grothendieck Theory of Dessins D'Enfants, London Math. Society Notes 200, Cambridge U. Press, Cambridge 1994, pp. 183-204.

  7. Leila Schneps, The Grothendieck-Teichmuller group and fundamental groups of moduli spaces, MSRI lecture available at http://www.msri.org/publications/ln/msri/1999/vonneumann/schneps/1/

    Grothendieck-Teichmueller group and Hopf algebras, MSRI lecture available at http://www.msri.org/publications/ln/msri/1999/vonneumann/schneps/2/

  8. Pierre Cartier, A mad day's work: from Grothendieck to Connes and Kontsevich - the evolution of concepts of space and symmetry, Bulletin of the AMS, 38 (2001), 389 - 408. Also available at http://www.ams.org/joursearch/index.html

  9. Jack Morava, The motivic Thom isomorphism, talk at the Newton Institute, December 2002, also available at arXiv:math.AT/0306151.

week202

  1. John Baez and Derek Wise, Quantization and Categorification.
    Fall 2003 notes: http://math.ucr.edu/home/baez/qg-fall2003
    Winter 2004 notes: http://math.ucr.edu/home/baez/qg-winter2004/
    Spring 2004 notes: http://math.ucr.edu/home/baez/qg-spring2004/

  2. Andreas Blass, Seven trees in one, Jour. Pure Appl. Alg. 103 (1995), 1-21. Also available at http://www.math.lsa.umich.edu/~ablass/cat.html

  3. Marcelo Fiore, Isomorphisms of generic recursive polynomial types, to appear in 31st Symposium on Principles of Programming Languages (POPL04). Also available at http://www.cl.cam.ac.uk/~mpf23/papers/Types/recisos.ps.gz

  4. Robbie Gates, On the generic solution to P(X) = X in distributive categories, Jour. Pure Appl. Alg. 125 (1998), 191-212.

  5. Marcelo Fiore and Tom Leinster, Objects of categories as complex numbers, available as arXiv:math.CT/0212377.

  6. Stephen H. Schanuel, What is the length of a potato?: an introduction to geometric measure theory, in Categories in Continuum Physics, Spring Lecture Notes in Mathematics 1174, Springer, Berlin, 1986, pp. 118-126.

  7. Stephen H. Schanuel, Negative sets have Euler characteristic and dimension, Lecture Notes in Mathematics 1488, Springer Verlag, Berlin, 1991, pp. 379-385.

  8. James Propp, Euler measure as generalized cardinality, available as arXiv:math.CO/0203289.

  9. James Propp, Exponentiation and Euler measure, available as arXiv:math.CO/0204009.

  10. Tom Leinster, Higher Operads, Higher Categories, Cambridge U. Press, Cambridge, 2003. Also available as arXiv:math.CT/0305049.

  11. Michael A. Batanin, The Eckmann-Hilton argument, higher operads and En spaces, available as arXiv:math.CT/0207281.

    Michael A. Batanin, The combinatorics of iterated loop spaces, available as arXiv:math.CT/0301221.

  12. Joachim Kock, Frobenius Algebras and 2D Topological Quantum Field Theories, Cambridge U. Press, Cambridge, 2003.

  13. Thomas Kerler and Volodymyr L. Lyubashenko, Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners, Lecture Notes in Mathematics 1765, Springer, Berlin, 2001.

  14. Thomas Kerler, Towards an algebraic characterization of 3-dimensional cobordisms, Contemp. Math. 318 (2003) 141-173. Also available as arXiv:math.GT/0008204.

  15. M. Laplaza, Coherence for distributivity, Lecture Notes in Mathematics 281, Springer Verlag, Berlin, 1972, pp. 29-72.

  16. G. Kelly, Coherence theorems for lax algebras and distributive laws, Lecture Notes in Mathematics 420, Springer Verlag, Berlin, 1974, pp. 281-375.

week203

  1. J. J. O'Connor and E. F. Robertson, The Golden Ratio, http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Golden_ratio.html

  2. Theodore A. Cook, The Curves of Life: Being an Account of Spiral Formations and Their Application to Growth in Nature, to Science, and to Art: with Special Reference to the Manuscripts of Leonardo da Vinci, Dover Publications, New York, 1979.

    David E. Joyce's edition of Euclid's Elements, http://aleph0.clarku.edu/~djoyce/java/elements/toc.html

  3. Oliver Byrne's edition of Euclid's Elements, online at the Digital Mathematics Archive, http://www.sunsite.ubc.ca/DigitalMathArchive/

  4. Thomas L. Heath's edition of Euclid's Elements, online at The Perseus Digital Library, http://www.perseus.tufts.edu/

  5. D. H. Fowler, The Mathematics of Plato's Academy: A New Reconstruction, Oxford U. Press, Oxford, 1987.

  6. Takashi Kanamaru and J. Michael T. Thompson, Introduction to Chaos and Nonlinear Dynamics, http://www.sekine-lab.ei.tuat.ac.jp/~kanamaru/Chaos/e/Standard/

  7. M. Tabor, Chaos and Integrability in Nonlinear Dynamics: An Introduction, Wiley, New York, 1989.

  8. Andre Katz, A short introduction to quasicrystallography, in From Number Theory to Physics, eds. M. Waldschmit et al, Springer, Berlin, 1992, pp. 496-537.

  9. Predrag Cvitanovic, Circle maps: irrationally winding, in From Number Theory to Physics, eds. M. Waldschmit et al, Springer, Berlin, 1992, pp. 631-658.

  10. Jean-Christophe Yoccoz, Introduction to small divisors problems, in From Number Theory to Physics, eds. M. Waldschmit et al, Springer, Berlin, 1992, pp. 659-679.

  11. W. Weisstein, Rogers-Ramanujan Continued Fraction, http://mathworld.wolfram.com/Rogers-RamanujanContinuedFraction.html

  12. G. H. Hardy, Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, Chelsea Publishing Co., New York, 1959.

  13. Michael Freedman, Michael Larsen, Zhenghan Wang, A modular functor which is universal for quantum computation, available at quant-ph/0001108.

  14. Paolo Boldi, Massimo Santini, and Sebastiano Vigna, Measuring with jugs, or: what if mathematicians were asked to defuse bombs?, Theoret. Comput. Sci. 2 (2002). Also available at http://vigna.dsi.unimi.it/papers.php

week204

  1. NGC 2359, the nebula around the Wolf-Rayet star HD56925, picture at http://cfa-www.harvard.edu/cfa/hotimage/n2359.html

  2. Sloan Digital Sky Survey, Evolutionary track of a sun-like star, http://skyserver.sdss.org/dr1/en/astro/stars/images/starevol.jpg

  3. The Messier Catalog, http://www.maa.agleia.de/Messier/

  4. The Messier Catalog, Planetary nebulae, http://www.maa.agleia.de/Messier/planetar.html

  5. The Messier Catalog, The crab nebula (M1), http://www.maa.agleia.de/Messier/E/m001.html

  6. Chris Clowes' Astronomy Page, http://www.peripatus.gen.nz/Astronomy/

  7. European Southern Observatory (ESO), Cosmological gamma-ray bursts and hypernovae conclusively linked, June 18, 2003, http://www.eso.org/outreach/press-rel/pr-2003/pr-16-03.html

  8. Burst and Transient Source Experiment (BATSE), GOTCHA! - The big one that didn't get away, January 27, 1999, http://www.batse.com/jan27.html

  9. NASA, gamma ray bursts,
  10. http://imagine.gsfc.nasa.gov/docs/introduction/bursts.html

  11. Edo Berger, Gamma-ray burst FAQ, http://www.astro.caltech.edu/~ejb/faq.html

  12. M. Livio, N. Panagia and K. Sahu, editors, Supernovae and Gamma-Ray Bursts: The Greatest Explosions since the Big Bang, Cambridge U. Press, 2001.

  13. Bradley W. Carroll and Dale A. Ostlie, Introduction to Modern Astrophysics, Addison Wesley, 1996.

  14. R. J. Tayler, The Stars: Their Structure and Evolution, 2nd edition, Cambridge U. Press, Cambridge, 1994.

  15. R. Kippenhahn and A. Weigert, Stellar Structure and Evolution, Springer Verlag, Berlin, 1991.

  16. John Baez, Stuff about Stars, http://math.ucr.edu/home/baez/stars.html

  17. John Baez, Open Questions in Physics, http://math.ucr.edu/home/baez/open.questions.html

week205

  1. James B. Kaler, The Hundred Greatest Stars, Copernicus Books (Springer Verlag), New York, 2002.

  2. Harold M. Stark, Galois theory, algebraic number theory, and zeta function, in From Number Theory to Physics, eds. M. Waldschmit et al, Springer, Berlin, 1992, pp. 313-393.

  3. Juergen Neukirch, Algebraic Number Theory, trans. Norbert Schappacher, Springer, Berlin, 1986.

  4. Z. I. Borevich and I. R. Shafarevich, Number Theory, trans. Newcomb Greenleaf, Academic Press, New York, 1966.

  5. Dino Lorenzini, An Invitation to Arithmetic Geometry, American Mathematical Society, Providence, Rhode Island, 1996.

  6. V. I. Danilov, V. V. Shokurov, and I. Shafarevich, Algebraic Curves, Algebraic Manifolds and Schemes, Springer, Berlin, 1998.

  7. David Eisenbud and Joe Harris, The Geometry of Schemes, Springer, Berlin, 2000.

  8. Stanley Burris and Karen Yeats, The saga of the high school identities, available at http://www.thoralf.uwaterloo.ca/htdocs/MYWORKS/preprints.html

  9. Antun Milas, Ramanujan's "Lost Notebook" and the Virasoro Algebra, available as math.QA/0309201.

week206

  1. Non Perturbative Quantum Gravity: Loops and Spin Foams, 3-7 May 2004, CIRM, Luminy, Marseille, France, http://w3.lpm.univ-montp2.fr/~philippe/quantumgravitywebsite/

  2. Leonard Susskind, The Landscape, article and interview on John Brockman's "EDGE" website, http://www.edge.org/3rd_culture/susskind03/susskind_index.html

  3. Jan Ambjorn, Jerzy Jurkiewicz and Renate Loll, Emergence of a 4d world from causal quantum gravity, available as arXiv:hep-th/0404156.

  4. Renate Loll, Discrete approaches to quantum gravity in four dimensions, available as arXiv:gr-qc/9805049 or as a website at Living Reviews in Relativity, http://www.livingreviews.org/Articles/Volume1/1998-13loll/

  5. Abhay Ashtekar, Donald Marolf, Jose Mourao and Thomas Thiemann, Constructing Hamiltonian quantum theories from path integrals in a diffeomorphism invariant context, Class. Quant. Grav. 17 (2000) 4919-4940. Also available as quant-ph/9904094.

  6. John Baez, Spin foam models, talk at Non Perturbative Quantum Gravity: Loops and Spin Foams, May 4, 2004, transparencies available at http://math.ucr.edu/home/baez/spin_foam_models/

  7. Jan Ambjorn, Jerzy Jurkiewicz and Renate Loll, Non-perturbative Lorentzian quantum gravity, causality and topology change, Nucl. Phys. B536 (1998) 407-434. Also available as arXiv:hep-th/9805108.

    Renate Loll and W. Westra, Space-time foam in 2d and the sum over topologies, Acta Phys. Polon. B34 (2003) 4997-5008. Also available as arXiv:hep-th/0309012.

  8. Jan Ambjorn, Jerzy Jurkiewicz and Renate Loll, Non-perturbative 3d Lorentzian quantum gravity, Phys.Rev. D64 (2001) 044011. Also available as arXiv:hep-th/0011276.

  9. Renate Loll, A discrete history of the Lorentzian path integral, Lecture Notes in Physics 631, Springer, Berlin, 2003, pp. 137-171. Also available as arXiv:hep-th/0212340.

  10. Laurent Freidel and David Louapre, Non-perturbative summation over 3D discrete topologies, Phys. Rev. D68 (2003) 104004. Also available as arXiv:hep-th/0211026.

  11. Laurent Freidel and David Louapre, Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles, available as arXiv:hep-th/0401076.

  12. Kirill Krasnov, Black hole thermodynamics and Riemann surfaces, Class. Quant. Grav. 20 (2003) 2235-2250. Also available as arXiv:gr-qc/0302073.

    Kirill Krasnov and Sergey N. Solodukhin, Effective stringy description of Schwarzschild black holes, available as arXiv:hep-th/0403046.

  13. Kirill Krasnov, Lambda<0 quantum gravity in 2+1 dimensions I: quantum states and stringy S-matrix, Class. Quant. Grav. 19 (2002) 3977-3998. Also available as arXiv:hep-th/0112164.

    Kirill Krasnov, Lambda<0 quantum gravity in 2+1 dimensions II: black hole creation by point particles, Class. Quant. Grav. 19 (2002) 3999-4028. Also available as arXiv:hep-th/0202117.

  14. Robert H. Sanders and Stacy S. McGaugh, Modified Newtonian Dynamics as an Alternative to Dark Matter, available as arXiv:astro-ph/0204521.

  15. Anthony Aguirre, Alternatives to dark matter (?), available as arXiv:astro-ph/0310572.

  16. The MOND pages, http://www.astro.umd.edu/~ssm/mond/litsub.html

  17. John Baez, Marseille, http://math.ucr.edu/home/baez/marseille/

week207

  1. GR17 homepage, http://www.dcu.ie/~nolanb/gr17.htm

  2. Roger Penrose, The Road To Reality: A Complete Guide to the Physical Universe, Jonathan Cape, 2004.

  3. Maximo Banados, Marc Henneaux, Claudio Teitelboim, and Jorge Zanelli, Geometry of the 2+1 black hole, Phys. Rev. D48 (1993) 1506-1525, also available as arXiv:gr-qc/9302012.

  4. Juan Maldacena, Eternal Black Holes in AdS, JHEP 0304 (2003) 021, also available as arXiv:hep-th/0106122.

  5. Juan Maldacena, Eternal Black Holes in AdS, http://online.itp.ucsb.edu/online/mtheory_c01/maldacena/.

  6. John Baez, Dublin, http://math.ucr.edu/home/baez/dublin/

week208

  1. Workshop on Quantum Gravity in the Americas, http://www.perimeterinstitute.ca/activities/scientific/PI-WORK-2/

  2. John Baez, The problem of dynamics in quantum gravity, http://math.ucr.edu/home/baez/dynamics/

  3. Lee Smolin, Fermions and topology, available as arXiv:gr-qc/9404010.

  4. John Baez and Kirill Krasnov, Quantization of diffeomorphism- invariant theories with fermions, arXiv:hep-th/9703112.

  5. Kirill Krasnov, Lambda<0 Quantum Gravity in 2+1 Dimensions I: Quantum States and Stringy S-Matrix, Class. Quant. Grav. 19 (2002) 3977-3998, also available as arXiv:hep-th/0112164.

    Kirill Krasnov, Lambda<0 Quantum Gravity in 2+1 Dimensions II: Black Hole Creation by Point Particles, Class. Quant. Grav. 19 (2002) 3999-4028, also available as arXiv:hep-th/0202117.

  6. Laurent Freidel and David Louapre, Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles, available as arXiv:hep-th/0401076.

    Laurent Freidel and David Louapre, Ponzano-Regge model revisited II: Equivalence with Chern-Simons, available as arXiv:gr-qc/0410141.

  7. Artem Starodubtsev, Topological excitations around the vacuum of quantum gravity I: The symmetries of the vacuum, available as arXiv:hep-th/0306135.

    Artem Starodubtsev and Lee Smolin, General relativity with a topological phase: an action principle, available as arXiv:hep-th/0311163.

  8. S. W. MacDowell and F. Mansouri, Unified geometric theory of gravity and supergravity, Phys. Rev. Lett. 38 (1977), 739-742.

  9. R. M. Kashaev, Quantization of Teichmueller spaces and the quantum dilogarithm, available as arXiv:q-alg/9705021.

  10. L. Chekhov and V. V. Fock, Quantum Teichmueller space, Theor. Math. Phys. 120 (1999) 1245-1259, also available as math.QA/9908165.

  11. Workshop on physics and geometry of 3-dimensional quantum gravity, http://www.ma.hw.ac.uk/~bernd/references.html

week209

  1. n-Categories: Foundations and Applications, http://www.ima.umn.edu/categories/

  2. Eugenia Cheng and Aaron Lauda, Higher-Dimensional Categories: an Illustrated Guide Book, available free online at: http://www.dpmms.cam.ac.uk/~elgc2/guidebook/

  3. John Baez, Why n-Categories? and What n-categories should be like. Notes available at http://www.ima.umn.edu/categories/#mon

  4. Tom Leinster, Survey and Taxonomy. Talk based on chapter 10 of his book Higher Operads, Higher Categories, Cambridge U. Press, Cambridge, 2004, also available free online at arXiv:math.CT/0305049.

  5. Andre Joyal, Peter May and Timothy Porter, Weak categories. Notes available at http://www.ima.umn.edu/categories/#tues

  6. Michael Batanin, Monoidal globular categories as natural environment for the theory of weak n-categories, Adv. Math. 136 (1998), 39-103, also available at http://www.ics.mq.edu.au/~mbatanin/papers.html

  7. Peter May, Model categories. Notes available at http://www.ima.umn.edu/categories/#wed

  8. Clemens Berger, Cellular definitions. Notes available at http://www.ima.umn.edu/categories/#wed

  9. Nick Gurski and Tom Leinster, Simplicial definition. Notes available at http://www.ima.umn.edu/categories/#thur

  10. Ross Street, Weak omega-categories, in Diagrammatic Morphisms and Applications, eds. David Radford, Fernando Souza, and David Yetter, Contemp. Math. 318, AMS, Providence, Rhode Island, 2003, pp. 207-213. Also available as www.maths.mq.edu.au/~street/Womcats.pdf

  11. Dominic Verity, Complicial sets, available as arXiv:math.CT/0410412

  12. Larry Breen, n-Stacks and n-gerbes: homotopy theory. Notes available at http://www.ima.umn.edu/categories/#thur

  13. David Corfield, n-Category theory as a catalyst for change in philosophy. Notes available at http://www.ima.umn.edu/categories/#fri

  14. Bertrand Toen, Segal categories. Notes by Joachim Kock available at http://www.ima.umn.edu/categories/#fri

  15. Bertrand Toen, n-Stacks and n-gerbes: algebraic geometry. Notes by Joachim Kock available at http://www.ima.umn.edu/categories/#fri

  16. Zbigniew Fiedorowicz, n-Fold categories. Notes available at http://www.ima.umn.edu/categories/#mon2

    C. Balteanu, Z. Fiedorowicz, R. Schwaenzl and R. Vogt, Iterated monoidal categories, available at arXiv:math.AT/9808082

    Z. Fiedorowicz, Constructions of En operads, available at arXiv:math.AT/9808089.

  17. Stefan Forcey, Higher enrichment: n-fold operads and enriched n-categories, delooping and weakening. Notes available at "http://www.ima.umn.edu/categories/#mon2

  18. Michael Makkai, On comparing definitions of weak n-category, available at http://www.math.mcgill.ca/makkai/

  19. Michael Makkai, The multitopic omega-category of all multitopic omega-categories, available at http://www.math.mcgill.ca/makkai/

  20. Mark Weber, Operads within monoidal pseudo algebras, available as arXiv:math.CT/0410230.

  21. Michael Batanin, The Eckmann-Hilton argument, higher operads and En-spaces, available at http://www.ics.mq.edu.au/~mbatanin/papers.html

    Michael Batanin, The combinatorics of iterated loop spaces, available at http://www.ics.mq.edu.au/~mbatanin/papers.html

  22. Joachim Kock, Topological quantum field theory primer. Notes available at http://www.ima.umn.edu/categories/#wed2

  23. Marco Mackaay, Topological quantum field theories. Notes available at http://www.ima.umn.edu/categories/#wed2

  24. John Baez, Space and state, spacetime and process. Notes available at http://www.ima.umn.edu/categories/#wed2

  25. Ross Street, An Australian conspectus of higher category theory. Notes available at http://www.ima.umn.edu/categories/#thur2

  26. Steve Lack, Higher model categories. Notes available at http://www.ima.umn.edu/categories/#thur2

  27. John Power, Why tricategories? Notes available at http://www.ima.umn.edu/categories/#thur2

  28. Philippe Gaucher, Towards a homotopy theory of higher dimensional automata. Notes available at http://www.ima.umn.edu/categories/#thur2

    Lisbeth Fajstrup, More on directed topology and concurrency, Notes available at http://www.ima.umn.edu/categories/#thur2

    Eric Goubault, Directed homotopy theory and higher-dimensional automata, Notes available at http://www.ima.umn.edu/categories/#thur2

  29. Alissa Crans, Higher linear algebra. Notes available at Notes available at http://www.ima.umn.edu/categories/#fri2

  30. John Baez, IMA, http://math.ucr.edu/home/baez/IMA/

  31. Francis Borceux and Enrico Vitale, Azumaya categories, available at http://www.math.ucl.ac.be/AGEL/Azumaya_categories.pdf

  32. Enrico Vitale, A Picard-Brauer exact sequence of categorical groups, Journal of Pure and Applied Algebra 175 (2002) 383-408. Also available as http://www.math.ucl.ac.be/membres/vitale/cat-gruppi2.pdf

  33. Alexander Grothendieck, Le groupe de Brauer. III. Exemples et complements. (French) 1968 Dix Exposes sur la Cohomologie des Schemas pp. 88-188 North-Holland, Amsterdam; Masson, Paris.

  34. Alexander Grothendieck, Le groupe de Brauer. II. Theorie cohomologique. (French) 1968 Dix Exposes sur la Cohomologie des Schemas pp. 67-87 North-Holland, Amsterdam; Masson, Paris.

  35. Alexander Grothendieck, Le groupe de Brauer. I. Algebres d'Azumaya et interpretations diverses. (French) 1968 Dix Exposes sur la Cohomologie des Schemas pp. 46-66 North-Holland, Amsterdam; Masson, Paris.

  36. Lindner, Harald, Morita equivalences of enriched categories. Conferences du Colloque sur l'Algebre des Categories (Amiens, 1973), III. Cahiers Topologie Geom. Differentielle 15 (1974), no. 4, 377-397, 449-450.

  37. J. Fisher-Palmquist and P. H. Palmquist, Morita contexts of enriched categories. Proc. Amer. Math. Soc. 50 (1975), 55-60.

  38. A. Froehlich, C. T. C. Wall, Graded monoidal categories. Compositio Math. 28 (1974), 229-285.

  39. A. Froehlich, C. T. C. Wall, Equivariant Brauer groups. Quadratic forms and their applications (Dublin, 1999), 57-71, Contemp. Math., 272, Amer. Math. Soc., Providence, RI, 2000.

  40. R. Gordon, A.J. Power and R. Street, Coherence for tricategories, Memoirs of the American Math. Society 117 (1995) Number 558.

  41. John W. Duskin, The Azumaya complex of a commutative ring. Categorical algebra and its applications (Louvain-La-Neuve, 1987), 107-117, Lecture Notes in Math., 1348, Springer, Berlin, 1988.

  42. John W. Duskin, An outline of a theory of higher-dimensional descent. Actes du Colloque en l'Honneur du Soixantieme Anniversaire de Rene Lavendhomme (Louvain-la-Neuve, 1989). Bull. Soc. Math. Belg. Ser. A 41 (1989), no. 2, 249-277.

  43. Categorical and combinatorial aspects of descent theory, Applied Categorical Structures (to appear; March 2003 preprint available at arXiv:math.CT/0303175).

  44. K.K. Ulbrich, Group cohomology for Picard categories, J. Algebra 91 (1984) 464-498.

  45. P. Carrasco and J. Martinez-Moreno, Simplicial cohomology with coefficients in symmetric categorical groups, Applied Categorical Structures 12 (2004), 257-286.

week210

  1. Huygens Probe Descent, http://saturn.jpl.nasa.gov/news/events/huygensDescent/index.cfm

  2. Arithmetic, Geometry and Topology: Conference on occasion of Larry Breen's sixtieth birthday, http://www-math.univ-paris13.fr/~lb2004/

  3. John Baez, Torsors made easy, http://math.ucr.edu/home/baez/torsors.html

  4. Paolo Aschieri, Luigi Cantini and Branislav Jurco, Nonabelian bundle gerbes, their differential geometry and gauge theory, available as arXiv:hep-th/0312154.

  5. Paolo Aschieri and Branislav Jurco, Gerbes, M5-brane anomalies and E8 gauge theory, available as arXiv:hep-th/0409200.

  6. Lawrence Breen, Bitorseurs et cohomologie non-abelienne, in The Grothendieck Festschrift, eds. P. Cartier et al, Progress in Mathematics vol. 86, Birkhauser, Boston, 1990, pp. 401-476.

  7. Lawrence Breen, Theorie de Schreier superieure, Ann. Sci. Ecole Norm. Sup. 25 (1992), 465-514.

  8. Lawrence Breen, Classification of 2-stacks and 2-gerbes, Asterisque 225, Societe Mathematique de France, 1994.

  9. Lawrence Breen and William Messing, The differential geometry of gerbes, available as arXiv:math.AG/0106083.

  10. Larry Breen, n-Stacks and n-gerbes: homotopy theory. Notes available at http://www.ima.umn.edu/categories/#thur

  11. John Baez and Aaron Lauda, Higher-dimensional algebra V: 2-groups, Theory and Applications of Categories 12 (2004), 423-491. Available online at http://www.tac.mta.ca/tac/volumes/12/14/12-14abs.html or as arXiv:math.QA/0307200.

  12. John Baez and Alissa Crans, Higher-dimensional algebra VI: Lie 2-algebras, Theory and Applications of Categories 12 (2004), 492-528. Available online at http://www.tac.mta.ca/tac/volumes/12/15/12-15abs.html or as arXiv:math.QA/0307263.

  13. Danny Stevenson, The geometry of bundle gerbes, Ph.D. thesis, University of Adelaide, 2000. Available as arXiv:math.DG/0004117.

  14. Michael K. Murray and Danny Stevenson, Higgs fields, bundle gerbes and string structures, Comm. Math. Phys. 236 (2003), 541-555. Also available as arXiv:math.DG/0106179.

  15. Alan L. Carey, Stuart Johnson, Michael K. Murray, Danny Stevenson and Bai-Ling Wang, Bundle gerbes for Chern-Simons and Wess-Zumino-Witten models, available as arXiv:math.DG/0410013.

  16. Toby Bartels, Categorified gauge theory: 2-bundles, available as arXiv:math.CT/0410328.

  17. Magnus Forrester-Barker, Representations of crossed modules and cat1-groups, Ph.D. thesis, Department of Mathematics, University of Wales, Bangor, 2004. Available at http://www.informatics.bangor.ac.uk/public/mathematics/research/ftp/theses/forrester-barker.pdf

  18. John Barrett and Marco Mackaay, Categorical representations of categorical groups, available as arXiv:math.CT/0407463.

  19. Josep Elgueta, Representation theory of 2-groups on finite dimensional 2-vector spaces, available as arXiv:math.CT/0408120.

  20. Louis Crane and David Yetter, Measurable categories and 2-groups, available as arXiv:math.QA/0305176.

  21. David Yetter, Measurable categories, available as arXiv:math.CT/0309185.

  22. Louis Crane and Marnie D. Sheppeard, 2-categorical Poincare representations and state sum applications, available as arXiv:math.QA/0306440.

  23. Hendryk Pfeiffer, Higher gauge theory and a non-Abelian generalization of 2-form electrodynamics, Annals Phys. 308 (2003), 447-477. Also available as arXiv:hep-th/0304074.

  24. Florian Girelli and Hendryk Pfeiffer, Higher gauge theory - differential versus integral formulation, Jour. Math. Phys. 45 (2004), 3949-3971. Also available as arXiv:hep-th/0309173.

  25. Hendryk Pfeiffer, 2-groups, trialgebras and their Hopf categories of representations, available as arXiv:math.QA/0411468.

  26. John Baez, Paris, http://math.ucr.edu/home/baez/paris/

week211

  1. Mars Express website, http://www.esa.int/SPECIALS/Mars_Express/index.html

  2. Mars Express sees signs of a "frozen sea", http://www.esa.int/SPECIALS/Mars_Express/SEMCHPYEM4E_0.html

  3. Glacial, volcanic and fluvial activity on Mars: latest images, http://www.esa.int/SPECIALS/Mars_Express/SEMLF6D3M5E_1.html

  4. John Milnor, Morse Theory, Princeton U. Press, Princeton, New Jersey, 1963.

  5. V. S. Varadarajan, Supersymmetry for Mathematicians: An Introduction, American Mathematical Society, Providence, Rhode Island, 2004.

  6. P. Deligne, P. Etingof, D.S. Freed, L. Jeffrey, D. Kazhdan, J. Morgan, D.R. Morrison and E. Witten, Quantum Fields and Strings: A Course For Mathematicians 2 vols., American Mathematical Society, Providence, 1999. Notes also available at http://www.math.ias.edu/QFT/

week212

  1. Pierre Deligne, Notes on spinors, in Quantum Fields and Strings: A Course For Mathematicians, volume 1, American Mathematical Society, Providence, 1999. Also available at http://www.math.ias.edu/QFT/fall/spinors.ps

  2. C. T. C. Wall, Graded Brauer groups, J. Reine Angew. Math. 213 (1963/1964), 187-199.

  3. Peter Donovan and Max Karoubi, Graded Brauer groups and K-theory with local coefficients, Publications Math. IHES 38 (1970), 5-25. Also available at http://www.math.jussieu.fr/~karoubi/Donavan.K.pdf

  4. R. W. Thomason, Symmetric categories model all connective spectra, Theory and Applications of Categories 1 (1995), 78-118. Available at http://www.tac.mta.ca/tac/volumes/1995/n5/1-05abs.html

  5. Michel Duflo, Operateurs differentiels bi-invariants sur un groupe de Lie, Ann. Sci. Ecole Norm. Sup. 10 (1977), 265-288.

  6. Dror Bar-Natan, Thang T. Q. Le and Dylan P. Thurston, Two applications of elementary knot theory to Lie algebras and Vassiliev invariants, Geometry and Topology 7 (2003), 1-31. Available at http://www.maths.warwick.ac.uk/gt/GTVol7/paper1.abs.html and also as arXiv:math.QG/0204311.

  7. Dylan P. Thurston, Wheeling: a diagrammatic analogue of the Duflo isomorphism, arXiv:math.QG/0006083.

  8. Pierre Deligne, letter to Dror Bar-Natan about the Duflo map, available at http://www.math.toronto.edu/~drorbn/Deligne/

week213

  1. Kenneth S. Brown, Cohomology of Groups, Graduate Texts in Mathematics 182, Springer, 1982.

  2. Jos Leys, Kleinian Pages, http://www.josleys.com/creatures42.htm

  3. David Mumford, Caroline Series, and David Wright, Indra's Pearls: The Vision of Felix Klein, Cambridge U. Press, Cambridge, 2002.

  4. Felix Klein and Arnold Sommerfeld, Über die Theorie des Kreisels, 4 vols, 1897-1910. Reprinted by Johnson, New York, 1965. Also available at http://www.hti.umich.edu/cgi/t/text/text-idx?c=umhistmath;idno=ABV7354.0001.001

  5. Felix Klein, The Mathematical Theory of the Top, Scribner's, New York, 1887.

  6. Felix Klein, Lectures on the Icosahedron and the Solution of Equations of the Fifth Degree, 1884. Reprinted by Dover, New York, 2003. Also available at http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=03070001&seq=7

  7. Jerry Shurman, Geometry of the Quintic, John Wiley and Sons, New York, 1997.

    Peter Doyle and Curt McMullen, Solving the quintic by iteration, Acta Math. 163 (1989), 151-180. Available at http://math.dartmouth.edu/~doyle/docs/icos/icos/icos.html

  8. John Baez, Fall 2004 Quantum Gravity Seminar, week 10, notes by Derek Wise, http://math.ucr.edu/home/baez/qg-fall2004/

  9. John Baez, Euler's Proof that 1+2+3+ ... = -1/12, Bernoulli Numbers and the Riemann Zeta Function, Winter 2004 Quantum Gravity Seminar, homework for weeks 5,6,7, available at http://math.ucr.edu/home/baez/qg-winter2004/

  10. G. Harder, A Gauss-Bonnet formula for discrete arithmetically defined groups, Ann. Sci. Ecole Norm. Sup. 4 (1971), 409-455.

  11. Jean-Pierre Serre, Cohomologie des groups discretes, Ann. Math. Studies 70 (1971), 77-169.

  12. Silvio Levy, The Eightfold Way: the Beauty of Klein's Quartic Curve, MSRI Research Publications 35, Cambridge U. Press, Cambridge 1999. Available at http://www.msri.org/publications/books/Book35/

week214

  1. Don Hatch, Hyperbolic planar tesselations, http://www.hadron.org/~hatch/HyperbolicTesselations/

  2. Tony Smith, Klein's quartic surface, http://www.valdostamuseum.org/hamsmith/cdomain.html#tesselations

  3. Silvio Levy, The Eightfold Way: the Beauty of Klein's Quartic Curve, MSRI Research Publications 35, Cambridge U. Press, Cambridge 1999. Also available as http://www.msri.org/publications/books/Book35/

  4. Tony Smith, Octonion products, http://www.valdostamuseum.org/hamsmith/480op.html

  5. Geoffrey Dixon, Octonion multiplication tables, http://www.7stones.com/Homepage/octotut0.html

  6. John Baez, review of "On Quaternions and Octonions: Their Geometry, Arithmetic and Symmetry", by John H. Conway and Derek A. Smith, Bull. Amer. Math. Soc. 42 (2005), 229-243. Available at http://www.ams.org/bull/2005-42-02/ and http://math.ucr.edu/home/baez/octonions/node24.html

  7. Ranee Brylinski and Bertram Kostant, Lagrangian models of minimal representations of E6, E7, and E8, in Functional Analysis on the Eve of the 21st Century, vol. 1, Progress in Math. 131, Birkhauser, Boston, 1995, pp. 13-53.

    Bertram Kostant, Minimal coadjoint orbits and symplectic induction, in The Breadth of Symplectic and Poisson geometry, 391-422, Progress in Math. 232, Birkhauser, Boston, 2005. Also available as http://www.arXiv.org/abs/math.SG/0312252

week215

  1. Greg Egan, Klein's quartic curve, http://math.ucr.edu/home/baez/KleinDual.gif

  2. Greg Egan, Turning Klein's quartic curve inside out, http://math.ucr.edu/home/baez/KleinDualInsideOut.gif

  3. Greg Egan, Cubes and anticubes in the Klein quartic curve, http://math.ucr.edu/home/baez/KleinFigures.gif

  4. Klein and Fricke, Klein's quartic curve with geodesic, http://math.ucr.edu/home/baez/Klein168.gif

  5. Jeff Stopple, A reciprocity law for prime geodesics, J. Number Theory 29 (1988), 224-230.

  6. Darin Brown, Lifting properties of prime geodesics on hyperbolic surfaces, Ph.D. thesis, U. C. Santa Barbara, 2004.

  7. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics, Springer, Berlin, 1990.

  8. Predrag Cvitanovic, Roberto Artuso, Per Dahlqvist, Ronnie Mainieri, Gregor Tanner, Gabor Vattay, Niall Whelan and Andreas Wirzba, Chaos: Classical and Quantum, available at http://www.nbi.dk/ChaosBook/

  9. Svetlana Katok, Fuchsian Groups, U. Chicago Press, Chicago, 1992.

  10. J. Elstrodt, F. Grunewald, and J. Mennicke, Groups Acting on Hyperbolic Space, Springer, Berlin, 1998.

  11. Peter Sarnak, Quantum chaos, symmetry and zeta functions, in Current Developments in Mathematics, 1997, eds R. Bott et al., International Press, Boston, 1999, pp. 127-159.

  12. C. Schmit, Quantum and classical properties of some billiards on the hyperbolic plane, in Chaos and Quantum Physics, eds. M.-J. Giannoni et al., Elsevier, New York, 1991, pp. 333-369.

  13. Martin Gutzwiller, Quantum chaos, Scientific American, January 1992. Also available at http://www.maths.ex.ac.uk/~mwatkins/zeta/quantumchaos.html

week216

  1. Matthew Watkins, Animation: the prime counting function π(x), http://www.maths.ex.ac.uk/~mwatkins/zeta/pianim.htm

  2. Xavier Gourdon, Computation of zeros of the Riemann zeta function, http://numbers.computation.free.fr/Constants/Miscellaneous/zetazeroscompute.html

  3. K. Sabbagh, Dr. Riemann's Zeros, Atlantic Books, 2002, pp. 134-136. Story about Hugh Montgomery and Freeman Dyson also available at http://www.maths.ex.ac.uk/~mwatkins/zeta/dyson.htm

  4. Matthew R. Watkins, A directory of all known zeta functions, http://www.maths.ex.ac.uk/~mwatkins/zeta/directoryofzetafunctions.htm

    Matthew R. Watkins, A directory of all known L-functions, http://www.maths.ex.ac.uk/~mwatkins/zeta/directoryofL-functions.htm

  5. Anton Deitman, Panorama of zeta functions, available as math.NT/0210060.

  6. Audrey Terras, Artin L-functions of graph coverings, available at http://math.ucsd.edu/~aterras/artin1.pdf

    More on L-functions, available at http://math.ucsd.edu/~aterras/artin2.pdf

  7. David Zywina, The zeta function of a graph, available at http://math.berkeley.edu/~zywina/zeta.pdf

week217

  1. Simon Singh, Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem, Walker, New York, 1997.

  2. Daniel Bump, Zeta Function, lecture notes on "the functional equation" available at http://math.stanford.edu/~bump/zeta.html and http://www.maths.ex.ac.uk/~mwatkins/zeta/fnleqn.htm

  3. Clay Mathematics Institute, Problems of the Millenium: the Riemann Hypothesis, http://www.claymath.org/millennium/

  4. Charles Daney, The Mathematics of Fermat's Last Theorem, http://www.mbay.net/~cgd/flt/fltmain.htm

  5. Runar Ile, Introduction to the Weil Conjectures, http://folk.uio.no/~ile/WeilA4.pdf

  6. James Milne, Lectures on Etale Cohomology, http://www.jmilne.org/math/CourseNotes/math732.html

  7. James Milne, Elliptic Curves, http://www.jmilne.org/math/CourseNotes/math679.html

  8. Serge Lang, Some history of the Shimura-Taniyama Conjecture, AMS Notices 42 (November 1995), 1301-1307. Available at http://www.ams.org/notices/199511/forum.pdf

  9. Henri Darmon, A proof of the full Shimura-Taniyama-Weil Conjecture is announced, AMS Notices 46 (December 1999), 1397-1401. Available at http://www.ams.org/notices/199911/comm-darmon.pdf

week218

  1. Alain Connes, Noncommutative Geometry, Trace Formulas, and the Zeros of the Riemann Zeta Function. Ohio State course notes and videos at http://www.math.ohio-state.edu/lectures/connes/Connes.html

    Alain Connes, Trace formula in noncommutative geometry and the zeros of the Riemann zeta function, available as arXiv:math.NT/9811068.

  2. Mathilde Marcolli, Noncommutative geometry and number theory, available at http://www.math.fsu.edu/~marcolli/ncgntE.pdf

  3. M. J. Shai Haran, The Mysteries of the Real Prime, Oxford U. Press, Oxford, 2001.

  4. Juergen Neukirch, Algebraic Number Theory, trans. Norbert Schappacher, Springer, Berlin, 1986.

  5. Dino Lorenzini, An Invitation to Arithmetic Geometry, American Mathematical Society, Providence, Rhode Island, 1996.

  6. John Baez and Derek Wise, Quantization and Categorification, available at:
    http://math.ucr.edu/home/baez/qg-fall2003/
    http://math.ucr.edu/home/baez/qg-winter2004/
    http://math.ucr.edu/home/baez/qg-spring2004/

  7. Martin H. Krieger, A 1940 letter of Andre Weil on analogy in mathematics, AMS Notices 52 (March 2005), 334-341. Available at http://www.ams.org/notices/200503/200503-toc.html

  8. Adam Sikora, Analogies between group actions on 3-manifolds and number fields, available as arXiv:math.GT/0107210.

  9. Christopher Deninger, A note on arithmetic topology and dynamical systems, available as arXiv:math.NT/0204274.

week219

  1. Categories in Algebra, Geometry and Mathematical Physics, conference in honor of the 60th birthday of Ross Street, http://streetfest.maths.mq.edu.au/

  2. John Baez, Higher gauge theory, http://math.ucr.edu/home/baez/street/

  3. Albert Einstein, On a heuristic viewpoint concerning the production and transformation of light, Annalen der Physik 17 (1905), 132-148. Available at http://dbserv.ihep.su/~elan/src/einstein05/eng.pdf

    On the movement of small particles suspended in stationary liquids required by the molecular-kinetic theory of heat, Annalen der Physik 17 (1905), 549-560. Available at http://lorentz.phl.jhu.edu/AnnusMirabilis/AeReserveArticles/eins_brownian.pdf

    On the electrodynamics of moving bodies, Annalen der Physik 17 (1905), 891-921. Available at http://dbserv.ihep.su/~elan/src/einstein05b/eng.pdf

    Does the inertia of a body depend upon its energy content?, Annalen der Physik 18 (1905), 639-641. Available at http://dbserv.ihep.su/~elan/src/einstein05c/eng.pdf

  4. Lee Smolin, Why no "new Einsteins"?, Physics Today, June 2005, 56-57.

  5. NASA, Pioneer path, http://spaceprojects.arc.nasa.gov/Space_Projects/pioneer/path.html

  6. Wikipedia, Pioneer anomaly, http://en.wikipedia.org/wiki/Pioneer_anomaly

  7. Chris P. Duif, Pioneer anomaly - literature and links, http://www.space-time.info/pioneer/pioanomlit.html

  8. The Pioneer Collaboration, A mission to explore the Pioneer anomaly, available as arXiv:gr-qc/0506139.

  9. Mark Wolverton, The Depths of Space: The Story of the Pioneer Planetary Probes, Joseph Henry Press, 2004. Available at http://www.nap.edu/books/0309090504/html/

  10. Intel, Silicon photonics, http://www.intel.com/technology/silicon/sp/

  11. Robert Service, Intel's breakthrough, Technology Review, July 2005, 62-65. Also available at http://www.technologyreview.com/articles/05/07/issue/feature_intel.asp

  12. Erika Jonietz, Quantum calculation, Technology Review, July 2005, 24-25. Also available at http://www.technologyreview.com/articles/05/07/issue/forward_quantum.asp

  13. Mike Stay, Klein quartic, http://math.ucr.edu/~mike/klein/

  14. Gerard Westendorp, Geometry, http://www.xs4all.nl/~westy31/Geometry/Geometry.html

  15. Joe Christy, Klein quartic pictures:
    http://math.ucr.edu/home/baez/pentacontihexahedron.jpg
    http://math.ucr.edu/home/baez/pentacontihexahedron2.jpg
    http://math.ucr.edu/home/baez/pentacontihexahedron3.jpg

  16. Joe Christy, Fano plane on Roman surface, http://math.ucr.edu/home/baez/roman.jpg

  17. John Baez, Klein's quartic curve, http://math.ucr.edu/home/baez/klein.html

  18. Ned Wright, Pioneer anomalous acceleration, http://www.astro.ucla.edu/~wright/PioneerAA.html

  19. Slava G. Turyshev, Michael Martin Nieto, and John D. Anderson, The Pioneer anomaly and its implications, available as gr-qc/0510081.

week220

  1. Leonard Susskind, The anthropic landscape of string theory, available as arXiv:hep-th/0302219.

  2. Abhay Ashtekar, Gravity and the quantum, available as arXiv:gr-qc/0410054.

  3. Abhay Ashtekar and Martin Bojowald, Black hole evaporation: a paradigm, Class. Quant. Grav. 22 (2005) 3349-3362. Also available as arXiv:gr-qc/0504029.

  4. Carlo Rovelli, Graviton propagator from background-independent quantum gravity, available as arXiv:gr-qc/0508124.

  5. Topics in Homotopy Theory, graduate summer school at the Pacific Institute of Mathematics run by Kristine Bauer and Laura Scull. Recommended reading material available at http://www.pims.math.ca/science/2005/05homotopy/reading.html

  6. Cafe π, http://www.cafepi.ca/

  7. J. Peter May, The Geometry of Iterated Loop Spaces, Lecture Notes in Mathematics 271, Springer, Berlin, 1972.

  8. J. Peter May, Infinite loop space theory, Bull. Amer. Math. Soc. 83 (1977), 456-494.

  9. Frederick Cohen, Homology of Ωn+1Σn+1X and Cn+1X, n > 0, Bull. Amer. Math. Soc. 79 (1973), 1236-1241.

  10. Frederick Cohen, Tom Lada and J. Peter May, The homology of iterated loop spaces, Lecture Notes in Mathematics 533, Springer, Berlin, 1976.

  11. Frederick Cohen, Tom Lada and J. Peter May, The homology of iterated loop spaces, Lecture Notes in Mathematics 533, Springer, Berlin, 1976.

  12. Dev Sinha, A pairing between graphs and trees, available as arXiv:math.QA/0502547.

  13. Dev Sinha, Manifold theoretic compactifications of configuration spaces, available as arXiv:math.GT/0306385.

  14. Maxim Kontsevich, Operads and motives in deformation quantization, Lett. Math. Phys. 48 (1999) 35-72. Also available as arXiv:math.QA/9904055.

  15. Ryan Budney and Frederick Cohen, On the homology of the space of long knots, available as arXiv:math.GT/0504206.

  16. Ryan Budney, Topology of spaces of knots in dimension 3, available as arXiv:math.GT/0506524.

week221

  1. Maria Rose Menocal, The Ornament of the World: How Muslims, Jews and Christians Created a Culture of Tolerance in Medieval Spain, Little, Brown and Co., 2002.

  2. Steve Edwards, Tilings from the Alhambra, http://www2.spsu.edu/math/tile/grammar/moor.htm

  3. John J. O'Connor and Edmund F. Robertson, Arabic mathematics: forgotten brilliance?, http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Arabic_mathematics.html

  4. John J. O'Connor and Edmund F. Robertson, Biographies of Arab/Islamic mathematicians, http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Arabs.html

  5. Charles Burnett, Leonard of Pisa and Arabic Arithmetic, http://muslimheritage.com/topics/default.cfm?ArticleID=472

  6. De Lacy O'Leary, How Greek Science Passed to the Arabs, Routledge & Kegan Paul Ltd, 1949. Also available at http://www.aina.org/books/hgsptta.htm

  7. Dimitri Gutas, Greek Thought, Arabic Culture: The Graeco-Arabic Translation Movement in Baghdad and Early 'Abbasid Society (2nd-4th/8th-10th Centuries), Routledge, 1998.

  8. Scott L. Montgomery, Science in Translation: Movements of Knowledge through Cultures and Time, U. of Chicago Press, 2000. Review by William R. Everdell available at MAA Online, http://www.maa.org/reviews/scitrans.html

  9. Stephen Gelbart: An elementary introduction to the Langlands program, Bulletin of the AMS 10 (1984), 177-219.

  10. Edward Frenkel, Recent advances in the Langlands program, available at arXiv:math.AG/0303074.

  11. Nova, The Archimedes Palimpsest, http://www.pbs.org/wgbh/nova/archimedes/palimpsest.html

  12. Heather Rock Woods, Placed under X-ray gaze, Archimedes manuscript yields secrets lost to time, Stanford Report, May 19, 2005, http://news-service.stanford.edu/news/2005/may25/archimedes-052505.html

  13. Erica Klarreich, Glimpses of genius: mathematicians and historians piece together a puzzle that Archimedes pondered, Science News 165 (2004), 314. Also available at http://www.sciencenews.org/articles/20040515/bob9.asp

  14. Julie Walker, A library of mud and ashes, BYU Magazine, Spring 2001, http://magazine.byu.edu/article.tpl?num=44-Spr01

  15. Oxyrhynchus Online, multispectral imaging, http://www.papyrology.ox.ac.uk/multi/procedure.html

week222

  1. Loops '05, http://loops05.aei.mpg.de

  2. Charles Stross, Accelerando, Ace Books, New York. Also available at http://www.accelerando.org/book/

  3. Wikipedia, Technological singularity, http://en.wikipedia.org/wiki/Technological_singularity

    Ray Kurzweil, The Singularity, http://www.kurzweilai.net/meme/frame.html?m=1

    Anders Sandberg, The Singularity, http://www.aleph.se/Trans/Global/Singularity/

  4. Official NASA Swift homepage, http://swift.gsfc.nasa.gov/docs/swift/swiftsc.html

  5. Gamma-ray burst real-time sky map, http://grb.sonoma.edu/

  6. D. B. Fox et al, The afterglow of GRB050709 and the nature of the short-hard γ-ray bursts, Nature 437 (October 2005), 849-850. Also available at http://www.nasa.gov/pdf/135397main_nature_fox_final.pdf

  7. Einstein@Home, http://einstein.phys.uwm.edu/

  8. European Southern Observatory, Black hole in search of a home, http://www.eso.org/outreach/press-rel/pr-2005/pr-23-05.html

    HubbleSite, Quasar without host galaxy compared with normal quasar, http://hubblesite.org/newscenter/newsdesk/archive/releases/2005/13/image/a

  9. Michael E. Brown, The moon of the 10th planet, http://www.gps.caltech.edu/~mbrown/planetlila/moon/index.html

  10. David C. Jewitt, Kuiper belt, http://www.ifa.hawaii.edu/faculty/jewitt/kb.html

  11. William Robert Johnston, Transneptunian objects, http://www.johnstonsarchive.net/astro/tnos.html

  12. Distant EKOs: the Kuiper Belt Electronic Newsletter, http://www.boulder.swri.edu/ekonews/

  13. Chad Trujillo, Quaoar, http://www.gps.caltech.edu/~chad/quaoar/

  14. David C. Jewitt and Jane Luu, Crystalline water ice on the Kuiper belt object (50000) Quaoar, Nature 432 (2004), 731-733. Also available at http://www.ifa.hawaii.edu/faculty/jewitt/quaoar.html

  15. Michael E. Brown, Chad A. Trujillo and David L. Rabinowitz, Discovery of a planetary-sized object in the scattered Kuiper belt, submitted to ApJ Letters, available at http://www.gps.caltech.edu/%7Embrown/papers/ps/xena.pdf

  16. Michael E. Brown, The discovery of UB313, the 10th planet, http://www.gps.caltech.edu/~mbrown/planetlila/

  17. Michael E. Brown, Chad A. Trujillo and David L. Rabinowitz, Discovery of a candidate inner Oort cloud planetoid, to appear in ApJ Letters, available at http://www.gps.caltech.edu/%7Embrown/papers/ps/sedna.pdf

  18. Michael E. Brown, Sedna (2003 VB12), http://www.gps.caltech.edu/~mbrown/sedna/

  19. Jan Ambjørn, J. Jurkiewicz and Renate Loll, Reconstructing the universe, Phys. Rev. D72 (2005) 064014. Also available as arXiv:hep-th/0505154.

  20. Jan Ambjørn, J. Jurkiewicz and Renate Loll, The universe from scratch, available as arXiv:hep-th/0509010.

  21. Oliver Lauscher and Martin Reuter, Fractal spacetime structure in asymptotically safe gravity, available as arXiv:hep-th/0508202.

  22. John Baez, Towards a spin foam model of quantum gravity, talk at Loops '05, available at http://math.ucr.edu/home/baez/loops05/

  23. John Barrett, Feynman diagams coupled to three-dimensional quantum gravity, available as arXiv:gr-qc/0502048.

    John Barrett, Feynman loops and three-dimensional quantum gravity, Mod. Phys. Lett. A20 (2005) 1271. Also available as arXiv:gr-qc/0412107.

  24. Laurent Freidel and David Louapre, Ponzano-Regge model revisited I: gauge fixing, observables and interacting spinning particles, Class. Quant. Grav. 21 (2004) 5685-5726. Also available as arXiv:hep-th/0401076.

    Laurent Freidel and David Louapre, Ponzano-Regge model revisited II: equivalence with Chern-Simons, available as arXiv:gr-qc/0410141

    Laurent Freidel and Etera R. Livine, Ponzano-Regge model revisited III: Feynman diagrams and effective field theory, available as arXiv:hep-th/0502106.

  25. Laurent Freidel, Daniele Oriti, and James Ryan, A group field theory for 3d quantum gravity coupled to a scalar field, available as arXiv:gr-qc/0506067.

  26. Karin Noui and Alejandro Perez, Three dimensional loop quantum gravity: coupling to point particles, available as arXiv:gr-qc/0402111.

  27. The Planetary Society, Pluto and Europa Campaign Page, http://www.planetary.org/html/UPDATES/Pluto/pluto_europa_action.html

  28. New Horizons: NASA's Pluto-Kuiper Belt Mission, http://pluto.jhuapl.edu/

  29. B. Garfinkel, On resonance in celestial mechanics: a survey, Celestial Mech. 28 (1982), 275-290, also available at http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1982CeMec..28..275G

  30. F. Varadi, M. Ghil, and W. M. Kaula, The great inequality in a planetary Hamiltonian theory, available as chao-dyn/9311011.

  31. Tetsuharu Fuse, Planetary perturbations on the 2:3 mean motion resonance with Neptune, Publ. Astron. Soc. Japan 54 (2002), 494-499. Also available at http://astronomy.nju.edu.cn/~xswan/reference/Fuse_PASJ54_493.pdf

  32. Luz Vianey Vela-Arevalo, Time-frequency analysis based on wavelets for Hamiltonian systems, Caltech, 2002. Also available at http://www.cds.caltech.edu/~luzvela/th2s.pdf

  33. George Voyatzis and John D. Hadjidemetriou, Symmetric and asymmetric librations in planetary and satellite systems at the 2/1 resonance, available at http://users.auth.gr/~hadjidem/Asymmetric1.pdf

    Mihailo Cubrovic, Regimes of stability and scaling relations for the removal time in the asteroid belt, available as astro-ph/0501004.

    Ryszard Gabryszewski and Ireneusz Wlodarczyk, The resonant dynamical evolution of small body orbits among giant planets, available as astro-ph/0203182.

    Luz V. Vela-Arevalo and Jerrold E. Marsden, Time-frequency analysis of the restricted three-body problem: transport and resonance transitions, Class. Quant. Grav. 21 (2004), S351-S375. Also available at http://cns.physics.gatech.edu/~luzvela/VelaArevaloMarsdenCQG_2004.pdf

    Harry Varvogli, Kleomenis Tsiganis, and John D. Hadjidemetriou, The "third" integral in the restricted three-body problem revisited, available at http://www.astro.auth.gr/~varvogli/varv5.ps

week223

  1. Cassini-Huyghens Mission, Hyperion: Odd World, http://saturn.jpl.nasa.gov/multimedia/images/image-details.cfm?imageID=1762

  2. Michael Berry, Chaos and the semiclassical limit of quantum mechanics (is the moon there when somebody looks?), in Quantum Mechanics: Scientific Perspectives on Divine Action, CTNS Publications, Vatican Observatory, 2001. Also available at http://www.phy.bris.ac.uk/people/berry_mv/the_papers/berry337.pdf

  3. The Hubble Heritage Project, Cat's Eye Nebula - NGC 6543, http://heritage.stsci.edu/2004/27/index.html

  4. Bruce Balick, Hubble Space Telescope images of planetary nebulae, http://www.astro.washington.edu/balick/WFPC2/index.html

  5. John Baez, A brief history of the universe, http://math.ucr.edu/home/baez/timeline.html

  6. Derek Wise, Electricity, magnetism and hypercubes, available at http://math.ucr.edu/~derek/talks/050916bw.pdf

  7. Miguel Carrion-Alvarez, Loop quantization versus Fock quantization of p-form electromagnetism on static spacetimes, available as math-ph/0412032.

  8. Derek Wise, Lattice p-form electromagnetism and chain field theory, available as arXiv:gr-qc/0510033. Version with better graphics and related material at http://math.ucr.edu/~derek/pform/index.html

  9. John Baez and Aaron Lauda, Higher-dimensional algebra V: 2-groups, Theory and Applications of Categories 12 (2004), 423-491. Available online at http://www.tac.mta.ca/tac/volumes/12/14/12-14abs.html or as arXiv:math.QA/0307200.

  10. O. Schreier, Ueber die Erweiterung von Gruppen I, Monatschefte fur Mathematik and Physick 34 (1926), 165-180. Ueber die Erweiterung von Gruppen II, Abh. Math. Sem. Hamburg 4 (1926), 321-346.

  11. P. Dedecker, Les foncteuers ExtΠ, H2Π and H2Π non abeliens, C. R. Acad. Sci. Paris 258 (1964), 4891-4895.

  12. Lawrence Breen, Theorie de Schreier superieure, Ann. Sci. Ecole Norm. Sup. 25 (1992), 465-514. Also available at http://www.numdam.org/numdam-bin/feuilleter?id=ASENS_1992_4_25_5

  13. V. Blanco, M. Bullejos and E. Faro, Categorical non abelian cohomology, and the Schreier theory of groupoids, available as arXiv:math.CT/0410202.

  14. Alexander Grothendieck, Revêtements Étales et Groupe Fondamental (SGA1), chapter VI: Catégories fibrées et descente, Lecture Notes in Mathematics 224, Springer, Berlin, 1971. Also available as math.AG/0206203.

  15. Wikipedia, Grothendieck universe, http://en.wikipedia.org/wiki/Grothendieck_universe

  16. Peter May, Classifying spaces and fibrations, Memoirs AMS 155, Jan. 1975.

  17. James Stasheff, Parallel transport in fibre spaces, Bol. Soc. Mat. Mexicana (1968), 68-86.

  18. James Stasheff, Associated fibre spaces, Michigan Math. Journal 15 (1968), 457-470.

  19. James Stasheff, H-spaces and classifying spaces, I-IV, AMS Proc. Symp. Pure Math. 22 (1971), 247-272.

  20. Ronald Brown and P. J. Higgins, Crossed complexes and non-abelian extensions, Category theory proceedings, Gummersbach, 1981, (ed. K.H. Kamps et al) Lecture Notes in Math. 962 Springer, Berlin, 1982, pp. 39-50.

  21. Ronald Brown and O. Mucuk, Covering groups of non-connected topological groups revisited, Math. Proc. Camb. Phil. Soc., 115 (1994) 97-110. Also available as arXiv:math.AT/0009021.

  22. Ronald Brown and Timothy Porter, On the Schreier theory of non-abelian extensions: generalisations and computations, Proceedings Royal Irish Academy 96A (1996), 213-227. Also available at http://www.informatics.bangor.ac.uk/public/math/research/ftp/algtop/rb/nonabex4.ps.gz

  23. Alan Turing, The extensions of a group, Compositio Mathematica 5 (1938), 357-367.

  24. Ronald Brown and Ilhan Icen, Homotopies and automorphisms of crossed modules of groupoids, Applied Categorical Structures, 11 (2003) 185-206. Also available as arXiv:math.CT/0008117.

  25. Ronald Brown and P. J. Higgins, The equivalence of ∞-groupoids and crossed complexes, Cah. Top. Geom. Diff. 22 (1981) 371-386.

  26. Ronald Brown and P. J. Higgins, The classifying space of a crossed complex, Math. Proc. Camb. Phil. Soc. 110 (1991) 95-120.

  27. Iakovos Androulidakis, Classification of extensions of principal bundles and transitive Lie groupoids with prescribed kernel and cokernel, J. Math. Phys. 45 (2004), 3095-4012. Also available as math.DG/0402007.

  28. Claudio Hermida, Descent on 2-fibrations and strongly 2-regular 2-categories, Applied Categorical Structures, 12 (2004), 427-459. Also available at http://maggie.cs.queensu.ca/chermida/papers/2-descent.pdf

week224

  1. Jet in M87, http://math.ucr.edu/home/baez/m87_jet.jpg

  2. NASA, MAXIM: Micro-Arcsecond X-ray Imaging Mission, http://maxim.gsfc.nasa.gov/docs/science/science.html

  3. A jet from galaxy M87, Astronomy Picture of the Day, July 6, 2000, http://antwrp.gsfc.nasa.gov/apod/ap000706.html

  4. M87: Chandra sheds light on the knotty problem of the M87 jet, http://chandra.harvard.edu/photo/2001/0134/

  5. Robert Lupton and the Sloan Digital Sky Survey Consortium, The central regions of M87, http://www.astro.princeton.edu/~rhl/PrettyPictures/

  6. Chris Mihos, Paul Harding, John Feldmeier and Heather Morrison, Deep imaging of the Virgo Cluster, http://burro.astr.cwru.edu/Schmidt/Virgo/

  7. The Hubble Heritage Project, Hoag's Object, http://heritage.stsci.edu/2002/21/

  8. Stephen W. Hawking, Information loss in black holes, available as arXiv:hep-th/0507171.

  9. John Baez, Dublin, http://math.ucr.edu/home/baez/dublin/

  10. Hamilton: two mysteries solved, http://groups.google.com/group/sci.physics/browse_thread/thread/d1b7b4a998682bbb/3a868ae8218a4bca#3a868ae8218a4bca

  11. William Rowan Hamilton, Second essay on a general method in dynamics, ed. David R. Wilkins, available at http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/Dynamics/SecEssay.pdf

  12. Jakob Palmkvist, A realization of the Lie algebra associated to a Kantor triple system, available as arXiv:math.RA/0504544.

  13. Bruce H. Bartlett, Categorical aspects of topological quantum field theories, M.Sc. Thesis, Utrecht University, 2005. Available as arXiv:math.QA/0512103.

  14. Aaron D. Lauda and Hendryk Pfeiffer, Open-closed strings: two-dimensional extended TQFTs and Frobenius algebras, available as arXiv:math.AT/0510664.

  15. Greg Moore, Lectures on branes, K-theory and RR charges, Clay Math Institute Lecture Notes (2002), available at http://www.physics.rutgers.edu/~gmoore/clay1/clay1.html

  16. Aaron Lauda, Frobenius algebras and ambidextrous adjunctions, available as arXiv:math.CT/0502550.

    Aaron Lauda, Frobenius algebras and planar open string topological field theories, arXiv:math.QA/0508349.

  17. Urs Schreiber, Lauda and Pfeiffer on open-closed topological strings, http://golem.ph.utexas.edu/string/archives/000680.html

  18. Ring around a galaxy, HubbleSite News Archive, May 6, 1999, http://hubblesite.org/newscenter/newsdesk/archive/releases/1999/16/image/a

  19. The lure of the rings, Hubblesite News Archive, April 22, 2004, http://hubblesite.org/newscenter/newsdesk/archive/releases/2004/15/image/a

  20. Doug Finkbeiner and the Sloan Digital Sky Survey Consortium, Some pretty objects as observed by the SDSS: Virgo Cluster, http://www.astro.princeton.edu/~rhl/dfink

  21. Ingo Runkel, Jens Fjelstad, Jurgen Fuchs and Christoph Schweigert, Topological and conformal field theory as Frobenius algebras, available as arXiv:math.CT/0512076.

week225

  1. Robert Dinwiddie, Philip Eales, David Hughes, Ian Nicholson, Ian Ridpath, Giles Sparrow, Pam Spence, Carole Stott, Kevin Tildsley, and Martin Rees, Universe, DK Publishing, New York, 2005.

  2. Richard Powell, An Atlas of the Universe, http://www.anzwers.org/free/universe/

  3. Bathsheba Grossman, Crystal model of a typical 100-megaparsec cube of the universe, http://www.bathsheba.com/crystal/largescale/

    Crystal model of the Milky Way, http://www.bathsheba.com/crystal/galaxy/

  4. R. Hurt, NASA/JPL-Caltech, Milky Way Bar, http://www.spitzer.caltech.edu/Media/mediaimages/sig/sig05-010.shtml

  5. Bathsheba Grossman, Mathematical models, http://www.bathsheba.com/math/

  6. Weisstein, Catenoid, from Mathworld, http://mathworld.wolfram.com/Catenoid.html

  7. Eric Weisstein, Helicoid, from Mathworld, http://mathworld.wolfram.com/Helicoid.html

  8. D. Hoffman, The computer-aided discovery of new embedded minimal surfaces, Mathematical Intelligencer 9 (1987), 8-21.

  9. GRAPE (Graphics Programming Environment), Surface overview, http://www-sfb256.iam.uni-bonn.de/grape/EXAMPLES/AMANDUS/bmandus.html

  10. GANG (Geometry Analysis Numerics Graphics), Gallery of minimal surfaces, http://www.gang.umass.edu/gallery/min/

  11. Elke Koch, 3-periodic minimal surfaces, http://staff-www.uni-marburg.de/~kochelke/minsurfs.htm

  12. Elke Koch and Werner Fischer, Mathematical crystallography http://www.staff.uni-marburg.de/~kochelke/mathcryst.htm#minsurf

  13. A. H. Schoen, Infinite periodic minimal surfaces without selfintersections, NASA Tech. Note No. D-5541, Washington, DC, 1970.

  14. Eric Weisstein, Gyroid, from Mathworld, http://mathworld.wolfram.com/Gyroid.html

  15. P. Garstecki and R. Holyst, Scattering patterns of self-assembled gyroid cubic phases in amphiphilic systems, J. Chem. Phys. 115 (2001), 1095-1099.

  16. Nelido Gonzalez-Segredo and Peter V. Coveney, Coarsening dynamics of ternary amphiphilic fluids and the self-assembly of the gyroid and sponge mesophases: lattice-Boltzmann simulations, available as cond-mat/0311002.

  17. Pittsburgh Supercomputing Center, Ketchup on the grid with joysticks, http://www.psc.edu/science/2004/teragyroid/

week226

  1. Geometry of Computation 2006 (Geocal06), http://iml.univ-mrs.fr/geocal06/

  2. Daniel Verschatse, Antilhue - Chile, NGC 1097 in Fornax, http://www.astrosurf.com/antilhue/ngc_1097_in_fornax.htm

  3. Spiral galaxy NGC 1097, European Southern Observatory, http://www.eso.org/outreach/press-rel/pr-2004/pr-28-04.html#phot-35d-04

  4. Mirror transport, European Southern Observatory, http://www.eso.org/outreach/press-rel/pr-1997/phot-35-97.html

  5. The southern sky above Paranal, European Southern Observatory, http://www.eso.org/outreach/press-rel/pr-2005/images/phot-40b-05-normal.jpg

  6. The VLT array on Paranal Mountain, European Southern Observatory, http://www.eso.org/outreach/press-rel/pr-2000/phot-14a-00-normal.jpg

  7. Feeding the monster, European Southern Observatory, http://www.eso.org/outreach/press-rel/pr-2005/phot-33-05.html

  8. Magnus Daum and Stefan Lucks, Attacking hash functions by poisoned messages: "The Story of Alice and Her Boss", http://www.cits.rub.de/MD5Collisions/

  9. Cryptographic hash function, Wikipedia, http://en.wikipedia.org/wiki/Cryptographic_hash

    Steve Friedl, An illustrated guide to cryptographic hashes, http://www.unixwiz.net/techtips/iguide-crypto-hashes.html

  10. SHA hash functions, Wikipedia, http://en.wikipedia.org/wiki/SHA_hash_functions

  11. Oded Goldreich, Foundations of Cryptography, Cambridge U. Press, Cambridge, 2004. Older edition available at http://www.wisdom.weizmann.ac.il/~oded/frag.html

  12. Clay Mathematics Institute, P vs NP problem, http://www.claymath.org/millennium/P_vs_NP/

  13. Random.org: random integer generator, http://random.org/

  14. NoEntropy.net: your online source for truly deterministic numbers, http://www.noentropy.net/

  15. Gregory Chaitin, Paradoxes of randomness, Complexity 7 (2002), 14-21. Also available as http://www.umcs.maine.edu/~chaitin/summer.html

  16. Oded Goldreich, papers and lecture notes on pseudorandomness, available at http://www.wisdom.weizmann.ac.il/~oded/pp_pseudo.html

    Luby, M. Pseudorandomness and Cryptographic Applications. Princeton, NJ: Princeton University Press, 1996.

  17. Anton Stiglic, Primes is in P little FAQ, http://crypto.cs.mcgill.ca/~stiglic/PRIMES_P_FAQ.html

  18. Luca Trevisian, Pseudorandomness and combinatorial constructions, available as cs.CC/0601100.

  19. Scott Aaronson, Is P versus NP formally independent?, available at http://www.scottaaronson.com/papers/pnp.pdf and http://www.scottaaronson.com/papers/pnp.ps

  20. Alexander A. Razborov and Steven Rudich, Natural proofs, in Journal of Computer and System Sciences, Vol. 55, No 1, 1997, pages 24-35. Also available at http://www-2.cs.cmu.edu/~rudich/papers/natural.ps and http://genesis.mi.ras.ru/~razborov/int.ps

  21. Alexander A. Razborov, Lower bounds for propositional proofs and independence results in bounded arithmetic, in Proceedings of ICALP 1996, 1996, pp. 48-62. Also available at http://genesis.mi.ras.ru/~razborov/icalp.ps

    R. Raz, P ≠ NP, propositional proof complexity, and resolution lower bounds for the weak pigeonhole principle, in Proceedings of ICM 2002, Vol. III, 2002, pp. 685-693. Also available at http://www.wisdom/weizmann.ac.il/~ranraz/publication/Pchina.ps

    S. Buss, Bounded arithmetic and propositional proof complexity, in Logic of Computation, ed. H. Schwictenberg, Springer-Verlag, 1997, pp. 67-122. Also available at http://www.wisdom/weizmann.ac.il/~ranraz/publication/Pchina.ps

  22. Uri Zwick, Boolean circuit complexity, http://www.math.tau.ac.il/~zwick/scribe-boolean.html

  23. Cristian Calude, Michael J. Dinneen, and Chi-Kou Shu, Computing a glimpse of randomness, Experimental Mathematics 11 (2002), 361-370. Also available at http://www.cs.auckland.ac.nz/~cristian/Calude361_370.pdf

  24. Leonid Levin, The tale of one-way functions, Problems of Information Transmission (= Problemy Peredachi Informatsii), 39 (2003), 92-103. Also available as cs.CR/0012023.

  25. Gregory Chaitin, Elegant LISP programs, in People and Ideas in Theoretical Computer Science, ed. C. Calude, Springer, Singapore, 1999, pp. 32-52. Also available at http://www.cs.auckland.ac.nz/CDMTCS/chaitin/lisp.html

  26. Peter Gacs, Lecture notes on descriptional complexity and randomness, available at http://www.cs.bu.edu/faculty/gacs/

  27. Adi Akavia, Oded Goldreich, Shafi Goldwasser and Dana Moshkovitz, On basing one-way functions on NP-hardness, November 22, 2005, available at http://theory.csail.mit.edu/~akavia/AGGM.pdf

  28. John Hastad, Russell Impagliazzo, Leonid A. Levin and Michael Luby, A pseudorandom generator from any one-way function, available at http://citeseer.ifi.unizh.ch/hastad99pseudorandom.html

  29. Scott Aaronson, Quantum lower bound for the collision problem, available as quant-ph/0111102.

  30. Yauyon Shi, Quantum lower bounds for the collision and the element distinctness problems, available as quant-ph/0112086.

  31. Electronic Colloquium on Computational Complexity, http://www.eccc.uni-trier.de/eccc/

  32. Scott Aaronson and Greg Kuperberg, Complexity Zoo, http://qwiki.caltech.edu/wiki/Complexity_Zoo

  33. Arjen K. Lenstra, Further progress in hashing cryptanalysis, February 26, 2005, available at http://cm.bell-labs.com/who/akl/hash.pdf

  34. Tony Stieber, GnuPG Hacks, Linux Journal, March 2006.

  35. Joel Spencer, The Strange Logic of Random Graphs, Springer, Berlin, 2001.

  36. John Baez, Recursivity in quantum mechanics, Trans. Amer. Math. Soc. 280 (1983), 339-350.

  37. Klaus Weihrauch and Ning Zhong Is wave propagation computable or can wave computers beat the Turing machine? Proc. Lond. Math. Soc. 85 (2002) 312-332. Abstract available at http://www.lms.ac.uk/publications/proceedings/abstracts/p1364a.html

  38. Susan Landau, Find me a hash, AMS Notices 53 (March 2006), 330-332. Also available at http://www.ams.org/notices/200603/fea-landau.pdf and http://www.ams.org/notices/200603/fea-landau.ps

week227

  1. Endurance crater's dazzling dunes, NASA/JPL, available at http://marsrovers.jpl.nasa.gov/gallery/press/opportunity/20040806a.html

  2. Mineral in Mars "berries" adds to water story, NASA/JPL, available at http://marsrover.nasa.gov/newsroom/pressreleases/20040318a.html

  3. Meme Therapy: Life from a science fiction point of view, http://memetherapy.blogspot.com/2006/03/brain-parade-feature-where-we-pester.html

  4. John Baez, Fundamental physics: where we stand today, lecture at at the Faculty of Sciences, Luminy, February 27th, 2006, available at http://math.ucr.edu/home/baez/where_we_stand/

  5. Varun Sahri, Dark matter and dark energy, available as arXiv:astro-ph/0403324.

  6. K. M. Heeger, Evidence for neutrino mass: a decade of discovery, available as arXiv:hep-ex/01412032.

  7. Geometry of Computation 2006 (Geocal06), http://iml.univ-mrs.fr/geocal06/

  8. Yves Lafont, Towards an algebraic theory of Boolean circuits, Journal of Pure and Applied Algebra 184 (2003), 257-310. Also available at http://iml.univ-mrs.fr/~lafont/publications.html

  9. Yves Lafont and A. Proute, Church-Rosser property and homology of monoids, Mathematical Structures in Computer Science, Cambridge U. Press, 1991, pp. 297-326. Also available at http://iml.univ-mrs.fr/~lafont/publications.html

  10. Albert Burroni, Higher dimensional word problem with application to equational logic, Theor. Comput. Sci. 115 (1993), 43-62. Also available at http://www.math.jussieu.fr/~burroni/

  11. Yves Guiraud, The three dimensions of proofs, Annals of Pure and Applied Logic (in press). Also available at http://iml.univ-mrs.fr/%7Eguiraud/recherche/cos1.pdf

  12. Francois Metayer, Resolutions by polygraphs, Theory and Applications of Categories 11 (2003), 148-184. Available online at http://www.tac.mta.ca/tac/volumes/11/7/11-07abs.html

  13. Francois Metayer, Resolutions by polygraphs, Theory and Applications of Categories 11 (2003), 148-184. Available online at http://www.tac.mta.ca/tac/volumes/11/7/11-07abs.html

  14. Philip J. Scott, Some aspects of categories in computer science, Handbook of Algebra, Vol. 2, ed. M. Hazewinkel, Elsevier, New York, 2000. Available as http://www.site.uottawa.ca/~phil/papers/

  15. John Baez, Universal algebra and diagrammatic reasoning, available as http://math.ucr.edu/home/baez/universal/

  16. Mauka Jibladze and Teimuraz Pirashvili, Cohomology of algebraic theories, J. Algebra 137 (1991) 253-296.

    Mauka Jibladze and Teimuraz Pirashvili, Quillen cohomology and Baues-Wirsching cohomology of algebraic theories, Max-Planck-Institut für Mathematik, preprint series 86 (2005).

  17. F. William Lawvere, Functorial Semantics of Algebraic Theories, Ph.D. thesis, Columbia University, 1963. Also available at http://www.tac.mta.ca/tac/reprints/articles/5/tr5abs.html

  18. R.A.G. Seely, Weak adjointness in proof theory, in Proc. Durham Conf. on Applications of Sheaves, Springer Lecture Notes in Mathematics 753, Springer, Berlin, 1979, pp. 697-701. Also available at http://www.math.mcgill.ca/rags/WkAdj/adj.pdf

    R.A.G. Seely, Modeling computations: a 2-categorical framework, in Proc. Symposium on Logic in Computer Science 1987, Computer Society of the IEEE, pp. 65-71. Also available at http://www.math.mcgill.ca/rags/WkAdj/LICS.pdf

  19. Vladimir Voevodsky, lectures on homotopy lambda calculus, notice at http://math.stanford.edu/distinguished_voevodsky.htm

week228

  1. North polar sand sea, Mars Odyssey Mission, THEMIS (Thermal emission imaging system), http://themis.mars.asu.edu/features/polardunes

  2. Wikipedia, Barchan, http://en.wikipedia.org/wiki/Barchan

  3. ESA/DLR/FU Berlin (G. Neukum), Glacial, volcanic and fluvial activity on Mars: latest images, http://www.esa.int/SPECIALS/Mars_Express/SEMLF6D3M5E_1.html

  4. NASA, Mars exploration program: dust storms, http://mars.jpl.nasa.gov/gallery/duststorms/

  5. NASA, Exploration rover mission: dust devils at Gusev, Sol 525, http://marsrovers.nasa.gov/gallery/press/spirit/20050819a.html

  6. Manfred R. Schroeder, Fractals, Chaos, Power Laws, W. H. Freeman, New York, 1992.

  7. Per Bak, Chao Tang and Kurt Wiesenfeld, Self-organized criticality: an explanation of 1/f noise, Phys. Rev. Lett. 59 (1987) 381-384.

  8. Jos Thijssen, The sand pile model and self organised criticality, http://www.tn.tudelft.nl/tn/People/Staff/Thijssen/sandexpl.html

  9. Albert Schueller, Cellular automaton sand pile model, http://schuelaw.whitman.edu/JavaApplets/SandPileApplet/

  10. Per Bak, How Nature Works: The Science of Self-Organized Criticality, Copernicus, New York, 1996.

  11. US Army Corps of Engineers, Dunes, http://www.tec.army.mil/research/products/desert_guide/lsmsheet/lsdune.htm

  12. V. Schwaemmle and H. J. Herrmann, Solitary wave behaviour of sand dunes, Nature 426 (Dec. 11, 2003), 619-620.

  13. Klaus Kroy, Gerd Sauermann, and Hans J. Hermann, Minimal model for sand dunes, Phys. Rev. Lett. 88 (2002), 054301. Also available at cond-mat/0101380.

  14. H. Elbelrhiti, P. Claudin, and B. Andreotti, Field evidence for surface-wave-induced instability of sand dunes, Nature 437 (Sep. 29, 2005), 720-723.

  15. Google Mars, http://www.google.com/mars/

  16. Jacques Distler, Unpleasantness, http://golem.ph.utexas.edu/~distler/blog/archives/000648.html

  17. Jay R. Goldman and Louis H. Kauffman, Rational tangles, Advances in Applied Mathematics 18 (1997), 300-332. Also available at http://www.math.uic.edu/~kauffman/RTang.pdf

  18. Louis H. Kauffman and Sofia Lambropoulou, On the classification of rational tangles, available as arXiv:math.GT/0311499.

  19. Edge of chaos, Wikipedia, http://en.wikipedia.org/wiki/Edge_of_chaos

week229

  1. Category Theory and its Applications: A Conference in Memory of Saunders Mac Lane, http://www.math.uchicago.edu/~may/MACLANE/

  2. Linda M. V. Martel, Ancient floodwaters and seas on Mars, http://www.psrd.hawaii.edu/July03/MartianSea.html

  3. M. H. Carr and J. W. Head, III, Oceans of Mars: An assessment of the observational evidence and possible fate, Journal of Geophysical Research 108 (2003), 5042.

  4. Perspective view of crater with water ice - looking east, ESA/DLR/FU Berlin (G. Neukum), http://www.esa.int/esa-mmg/mmg.pl?b=b&type=I&mission=Mars%20Express&single=y&start=53

  5. Carlos A. Furuti, Conformal projections, http://www.progonos.com/furuti/MapProj/Normal/ProjConf/projConf.html

  6. Igor V. Dolgachev, Lectures on modular forms, Fall 1997/8, available at http://www.math.lsa.umich.edu/~idolga/modular.pdf

  7. Quincunx, World Wide Words, http://www.worldwidewords.org/weirdwords/ww-qui2.htm

week230

  1. A moment frozen in time, NASA Mars Exploration Rover Mission, http://marsrovers.nasa.gov/gallery/press/spirit/20050610a.html

  2. C. S. Calude and M. A. Stay, From Heisenberg to Goedel via Chaitin, International Journal of Theoretical Physics, 44 (2005), 1053-1065. Also available at http://math.ucr.edu/~mike/

  3. Jonathan Sondow, A faster product for pi and a new integral for ln(pi/2), Amer. Math. Monthly 112 (2005), 729-734. Also available as arXiv:math.NT/0401406.

  4. Abelian categories, Wikipedia, http://en.wikipedia.org/wiki/Abelian_category

  5. Peter Freyd, Abelian Categories, Harper and Row, New York, 1964. Also available at http://www.tac.mta.ca/tac/reprints/articles/3/tr3abs.html

  6. G. Gonzalez-Springberg and J. L. Verdier, Construction geometrique de la correspondance de McKay, Ann. ENS 16 (1983), 409-449.

  7. Mikhail Kapranov and Eric Vasserot, Kleinian singularities, derived categories and Hall algebras, available as arXiv:math.AG/9812016.

  8. Andrei Gabrielov, Coxeter-Dynkin diagrams and singularities, in Selected Ppaers of E. B. Dynkin with Commentary, eds. A. A. Yushkevich, G. M. Seitz and A. I. Onishchik, AMS, 1999. Also available at http://www.math.purdue.edu/~agabriel/dynkin.pdf

  9. John McKay, A rapid introduction to ADE theory, http://math.ucr.edu/home/baez/ADE.html

  10. Joris van Hoboken, Platonic solids, binary polyhedral groups, Kleinian singularities and Lie algebras of type A,D,E, Master's Thesis, University of Amsterdam, 2002, available at http://home.student.uva.nl/joris.vanhoboken/scriptiejoris.ps or http://math.ucr.edu/home/baez/joris_van_hoboken_platonic.pdf

  11. M. Hazewinkel, W. Hesselink, D. Siermsa, and F. D. Veldkamp, The ubiquity of Coxeter-Dynkin diagrams (an introduction to the ADE problem), Niew. Arch. Wisk., 25 (1977), 257-307. Also available at http://repos.project.cwi.nl:8888/cwi_repository/docs/I/10/10039A.pdf or http://math.ucr.edu/home/baez/hazewinkel_et_al.pdf

  12. Jerry Michael Shurman, Geometry of the Quintic, Wiley, New York, 1997.

  13. P. Slodowy, Simple Singularities and Algebraic Groups, Lecture Notes in Mathematics 815, Springer, Berlin, 1980.

  14. Miles Reid, Links to papers on McKay correspondence, http://www.maths.warwick.ac.uk/~miles/McKay/

  15. Miles Reid, La Correspondence de McKay (in English), Seminaire Bourbaki, 52eme annee, November 1999, no. 867, to appear in Asterisque 2000. Also available as arXiv:math.AG/9911165.

  16. Michael R. Douglas and Gregory Moore, D-branes, quivers and ALE instantons, available as arXiv:hep-th/9603167.

  17. Harm Derksen and Jerzy Weyman, Quiver representations, AMS Notices 52 (2005), 200-206. Also available as http://www.ams.org/notices/200502/fea-weyman.pdf

  18. Idun Reiten, Dynkin diagrams and the representation theory of algebras, AMS Notices 44 (1997), 546-556.

  19. John Milnor, Singular points of complex hypersurfaces, Ann. Math. Studies 61, Princeton U. Press, Princeton, 1968.

  20. H. S. M. Coxeter, The evolution of Coxeter-Dynkin diagrams, in: T. Bisztriczky, P. McMullen, R. Schneider, A. Ivic Weiss, eds., Polytopes: Abstract, Convex and Computational, NATO ASI Series C, Vol. 440, Kluwer, Dordrecht, 1994, pp. 21-42.

  21. E. Witt, Spiegelungsgruppen und Aufzahlung halbeinfacher Liescher Ringe. Abhandl. Math. Sem. Univ. Hamburg. 14 (1941), 289-337.

week231

  1. NASA, Enceladus the storyteller, http://www.nasa.gov/mission_pages/cassini/multimedia/pia07800.html

  2. NASA's Cassini discovers potential liquid water on Enceladus, http://saturn.jpl.nasa.gov/news/press-release-details.cfm?newsID=639

  3. Special issue on Enceladus, Science 311 (March 10th 2006).

  4. NASA, Enceladus "cold geyser" model, http://www.nasa.gov/mission_pages/cassini/multimedia/pia07799.html

  5. Martin Chaplin, Forty-one anomalies of water, http://www.lsbu.ac.uk/water/anmlies.html

  6. Martin Chaplin, The phase diagram of water, http://www.lsbu.ac.uk/water/phase.html

  7. Diamond anvil cell, Wikipedia, http://en.wikipedia.org/wiki/Diamond_Anvil_Cell

  8. Light gas gun, Wikipedia, http://en.wikipedia.org/wiki/Light_Gas_Gun

  9. Robert C. Cauble, Putting more pressure on hydrogen, http://www.llnl.gov/str/Cauble.html

  10. Carlo Cavazzoni, Large scale first-principles simulations of water and ammonia at high pressure and temperature, Ph.D. thesis, Scuola Internazionale Superiore di Studi Avanzati, October 1998. Figure 4.10: symmetric and super-ionic ice X structures, p. 57. Available at http://sirio.cineca.it/~acv0/thesis.html

  11. C. Cavazzoni, G. L. Chiarotti, S. Scandolo, E. Tosatti, M. Bernasconi and M. Parrinello, Superionic and metallic states of water and ammonia at giant planet conditions, Science 283 (January 1999), 44-46. Also available at http://www.sciencemag.org/cgi/content/full/283/5398/44

  12. P. M. Celliers et al, Electronic conduction in shock-compressed water, Plasmas 11 (2004), L41-L48.

  13. Nancy McGuire, The many phases of water, American Chemical Society, https://web.archive.org/web/20051201104533/http://www.chemistry.org/portal/a/c/s/1/feature_pro.html?id=c373e9fbed0a01c78f6a4fd8fe800100

  14. J. L. Finney, The phase diagram of water and a new metastable form of ice, http://www.cmmp.ucl.ac.uk/people/finney/soi.html

  15. Koichiro Umemoto, Renata M. Wentzcovitch, Stefano Baroni and Stefano de Cironcoli, Anomalous pressure-induced transition(s) in ice XI, Physical Review Letters 92 (2004), 105502-1. Also available at http://www.cems.umn.edu/research/wentzcovitch/papers/Phys._Rev._Lett._92_105502_(2004).pdf

  16. Mariana Gosnell, Ice: The Nature, the History, and the Uses of an Astonishing Substance, Alfred A. Knopf, New York, 2005.

  17. Mark Bowen, Thin Ice: Unlocking the Secrets of Climate in the World's Highest Mountains, Henry Holt & Co., 2005.

  18. Urs Schreiber, A note on RCFT and quiver reps, http://golem.ph.utexas.edu/string/archives/000794.html

  19. Paul Aspinwall, D-branes on Calabi-Yau manifolds, section 7.3.1, The McKay correspondence, p. 101 and following. Available as arXiv:hep-th/0403166

  20. David J. Benson, Representations and Cohomology I, Cambridge U. Press, Cambridge 1991.

  21. P. Gabriel and A. V. Roiter, Representations of Finite-Dimensional Algebras, Enc. of Math. Sci., 73, Algebra VIII, Springer, Berlin 1992.

  22. Tom Bridgeland, Alaistair King and Miles Reid, Mukai implies McKay: the McKay correspondence as an equivalence of derived categories, available as arXiv:math.AG/9908027.

  23. Tom Bridgeland, T-structures on some local Calabi-Yau varieties, available as arXiv:math.AG/0502050.

  24. Aaron Bergman, Undoing orbifold quivers, available as arXiv:hep-th/0502105.

    Aaron Bergman, Moduli spaces for Bondal quivers, available as arXiv:math.AG/0512166.

week232

  1. Steve Yunck / NSF, Cerenkov light passing through the IceCube neutrino detector, http://icecube.wisc.edu/gallery/detector_concepts/ceren_hires

  2. Darwin Rianto / NSF, Comparison of AMANDA and IceCube, http://icecube.wisc.edu/gallery/detector_concepts/icecubeencomp_300

  3. Robert G. Stokstad / NSF, South Pole Station, http://icecube.wisc.edu/gallery/antarctica/PC140287_300

  4. Ice Cube turns up the heat, The Antarctic Sun, January 29, 2006, http://antarcticsun.usap.gov/2005-2006/contentHandler.cfm?id=959

  5. Francis Halzen, Ice fishing for neutrinos, http://icecube.berkeley.edu/amanda/ice-fishing.html

  6. Katie Yurkiewicz, Extreme neutrinos, Symmetry, volume 1 issue 1, November 2004, http://symmetrymagazine.org/cms/?pid=1000014

  7. M. Ackermann et al, Search for extraterrestrial point sources of high energy neutrinos with AMANDA-II using data collected in 2000-2002, available as arXiv:astro-ph/0412347.

  8. AMANDA II Project, http://amanda.uci.edu/

  9. Welcome to IceCube, http://icecube.wisc.edu/

  10. Davide L. Ferrario, Periodic orbits for the 60-body problem, http://www.matapp.unimib.it/~ferrario/mov/index.html

  11. Davide L. Ferrario and S. Terracini, On the existence of collisionless equivariant minimizers for the classical n-body problem. Invent. Math. 155 (2004), 305-362.

  12. John Baez, Derek Wise and Alissa Crans, Exotic statistics for strings in 4d BF theory, available as arXiv:gr-qc/0603085.

  13. John Baez and Alejandro Perez, Quantization of strings and branes coupled to BF theory, available as arXiv:gr-qc/0605087.

  14. Phillipp de Sousa Gerbert, On spin and (quantum) gravity in 2+1 dimensions, Nuclear Physics B346 (1990), 440-472.

  15. Laurent Freidel, Jerzy Kowalski-Glikman and Lee Smolin, 2+1 gravity and doubly special relativity, Phys. Rev. D69 (2004) 044001. Also available as arXiv:hep-th/0307085.

week233

  1. Sundance O. Bilson-Thompson, A topological model of composite preons, available as arXiv:hep-ph/0503213.

  2. Sundance O. Bilson-Thompson, Fotini Markopoulou, and Lee Smolin, Quantum gravity and the Standard Model, arXiv:hep-th/0603022.

  3. Imre Tuba and Hans Wenzl, Representations of the braid group B3 and of SL(2,Z), available as arXiv:math.RT/9912013.

  4. Terry Gannon, The algebraic meaning of genus-zero, available as arXiv:math.NT/0512248.

  5. Yongchang Zhu, Modular invariance of characters of vertex operator algebras, J. Amer. Math. Soc 9 (1996), 237-302. Also available at http://www.ams.org/jams/1996-9-01/S0894-0347-96-00182-8/home.html

  6. Brian Sanderson, The knot theory MA3F2 page, http://www.maths.warwick.ac.uk/~bjs/MA3F2-page.html

  7. R. Voituriez, Random walks on the braid group B3 and magnetic translations in hyperbolic geometry, Nucl. Phys. B621 (2002), 675-688. Also available as http://arxiv.org/abs/math-ph/0103008.

  8. John Milnor, Introduction to Algebraic K-theory, Annals of Math. Studies 72, Princeton U. Press, Princeton, New Jersey, 1971.

week234

  1. Cris Moore, The 3-body (and n-body) problem, http://www.santafe.edu/~moore/gallery.html

  2. Cristopher Moore and Michael Nauenberg, New periodic orbits for the n-body problem, available at arXiv:math.DS/0511219.

  3. Thomas M. Fiore, Music and mathematics, available at http://www.math.uchicago.edu/~fiore/1/music.html

  4. Thomas M. Fiore and Ramon Satyendra, Generalized contextual groups, Music Theory Online 11 (2005), available at http://www.math.uchicago.edu/~fiore/1/music.html

  5. Joe Monzo, Tonnetz: the tonal lattice invented by Riemann, Tonalsoft: the Encyclopedia of Microtonal Music Theory, http://www.tonalsoft.com/enc/t/tonnetz.aspx

  6. Paul Dysart, Tonnetz: musics, harmony and donuts, http://members2.boo.net/~knuth/

  7. John Baez, Torsors made easy, http://math.ucr.edu/home/baez/torsors.html

  8. David Lewin, Generalized Musical Intervals and Transformations, Yale University Press, New Haven, Connecticut, 1987.

  9. Julian Hook, Uniform Triadic Transformations, Ph.D. thesis, Indiana University, 2002.

  10. Adrian P. Childs, Moving beyond neo-Riemannian triads: exploring a transformational model for seventh chords, Journal of Music Theory 42/2 (1998), 191-193.

  11. Edward Gollin, Some aspects of three-dimensional Tonnetze, Journal of Music Theory 42/2 (1998), 195-206.

  12. Richard Cohn, Neo-Riemannian operations, parsimonious trichords, and their "Tonnetz" representations, Journal of Music Theory 41/1 (1997), 1-66.

  13. David Lewin, Transformational considerations in Schoenberg's Opus 23, Number 3, preprint.

  14. Stephen Lavelle, Some formalizations in musical set theory, June 3, 2005, available at http://www.maths.tcd.ie/~icecube/lewin.pdf and http://www.maths.tcd.ie/~icecube/lewin.ps

  15. Music Theory Online, http://mto.societymusictheory.org/

  16. Society for Music Theory, Fundamentals of music theory, selected bibliography, http://societymusictheory.org/index.php?pid=37

  17. Wikipedia, Musical set theory, http://en.wikipedia.org/wiki/Musical_set_theory

  18. Dmitri Tymoczko, ChordGeometries, http://music.princeton.edu/~dmitri/ChordGeometries.html

  19. Dmitri Tymoczko, Scale theory, serial theory, and voice leading, available at http://music.princeton.edu/~dmitri/scalesarrays.pdf

  20. Steven H. Cullinane, Geometry of the 4 × 4 square, http://finitegeometry.org/sc/16/geometry.html

  21. Peter J. Cameron, Projective and Polar Spaces, QMW Math Notes 13, 1991. Also available at http://www.maths.qmul.ac.uk/~pjc/pps/ Chapter 9: The geometry of the Mathieu groups, available at http://www.maths.qmul.ac.uk/~pjc/pps/pps9.pdf

  22. David Richter, How to make the Mathieu group M24, http://homepages.wmich.edu/~drichter/mathieu.htm

  23. Dave Rusin, Mathematics and music, http://www.math.niu.edu/~rusin/uses-math/music/

  24. Guerino Mazzola, The Topos of Music: Geometric Logic of Concepts, Theory and Performance, Birkhauser, Berlin, 2002. Preface and contents available at http://www.encyclospace.org/tom/tom_preface_toc.pdf

    Guerino Mazzola, homepage, http://www.ifi.unizh.ch/staff/mazzola/mazzola.html

  25. John H. Conway, Noam D. Elkies, Jeremy L. Martin, The Mathieu group M12 and its pseudogroup extension M13, available as arXiv:math.GR/0508630.

  26. William Sethares, Relating tuning and timbre, http://eceserv0.ece.wisc.edu/~sethares/consemi.html

  27. William Sethares, MP3 Download Central, http://eceserv0.ece.wisc.edu/~sethares/otherperson/all_mp3s.html

  28. William Sethares, Tuning, Timbre, Spectrum, Scale, 2nd edition, Springer Verlag, Berlin, 2004. Author's guide available at http://eceserv0.ece.wisc.edu/~sethares/ttss.html. Sound examples available at http://eceserv0.ece.wisc.edu/~sethares/html/soundexamples.html

  29. John Rahn, Music 575: Music and Mathematics, November 2004, syllabus available at http://faculty.washington.edu/jrahn/5752004.htm

  30. Ken Gewertz, Composer, music theorist David Lewin dies at 69, Harvard University Gazette, http://www.news.harvard.edu/gazette/2003/05.15/13-lewinobit.html

  31. Harald Fripertinger, Mathematical music theory, http://www.uni-graz.at/~fripert/index_11.html

  32. Thomas Noll, The topos of triads, available at http://www.cs.tu-berlin.de/~noll/ToposOfTriads.pdf

  33. Guerino Mazzola and Moreno Andreatta, From a categorical point of view: K-nets as limit denotators, available at recherche.ircam.fr/equipes/repmus/mamux/documents/mazzola-andreatta.pdf

  34. Maria Jose Garmendia Rodriguez and Juan Antonio Navarro Gonzalez, Musical scales, IMS Bulletin 35 (Christmas 1995), 24.

week235

  1. Institute for Quantum Computing (IQC), http://www.iqc.ca/

  2. Jonathan Baugh, Osama Moussa, Colm A. Ryan, Raymond Laflamme, Chandrasekhar Ramanathan, Timothy F. Havel and David G. Cory, Solid-state NMR three-qubit homonuclear system for quantum information processing: control and characterization, Phys. Rev. A 73 (2006), 022305. Also available as quant-ph/0510115.

  3. Artur Ekert, Cracking codes, part II, Plus Magazine, http://pass.maths.org.uk/issue35/features/ekert/index.html

  4. IQC, Free-space quantum key distribution, http://www.iqc.ca/laboratories/peg/free_space.php

  5. Wikipedia, Liouville's theorem (Hamiltonian), http://en.wikipedia.org/wiki/Liouville's_theorem_(Hamiltonian)

  6. Michael A. Nielsen and Isaac L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, 2000.

  7. John Preskill, Quantum computation - lecture notes, references etc. at http://www.theory.caltech.edu/people/preskill/ph229/

  8. John Preskill, Fault-tolerant quantum computation, to appear in "Introduction to Quantum Computation", eds. H.-K. Lo, S. Popescu, and T. P. Spiller. Also available as quant-ph/9712048.

  9. Peter Shor, Fault-tolerant quantum computation, 37th Symposium on Foundations of Computing, IEEE Computer Society Press, 1996, pp. 56-65. Also available as quant-ph/9605011.

  10. Dorit Aharonov and Michael Ben-Or, Fault-tolerant quantum computation with constant error rate, available as quant-ph/9906129.

  11. Barbara M. Terhal and Guido Burkard, Fault-tolerant quantum computation for local non-markovian noise, Phys. Rev. A 71, 012336 (2005). Also available as quant-ph/0402104.

  12. H. S. Leff and Andrew F. Rex, editors, Maxwell's Demon: Entropy, Information and Computing, Institute of Physics Publishing, 1990.

  13. Scott Aaronson, NP-complete problems and physical reality, ACM SIGACT News, March 2005. Also available as quant-ph/0502072.

  14. Aristide Baratin and Laurent Freidel, Hidden quantum gravity in 4d Feynman diagrams: emergence of spin foams.

  15. Aristide Baratin and Laurent Freidel, Hidden quantum gravity in 3d Feynman diagrams. Available as arXiv:gr-qc/0604016.

  16. Laurent Freidel, Jerzy Kowalski-Glikman and Artem Starodubtsev, Particles as Wilson lines in the gravitational field, available as arXiv:gr-qc/0607014.

  17. John Baez, An introduction to spin foam models of BF theory and quantum gravity, in Geometry and Quantum Physics, eds. Helmut Gausterer and Harald Grosse, Lecture Notes in Physics, Springer-Verlag, Berlin, 2000, pp. 25-93. Also available as arXiv:gr-qc/9905087.

  18. John Baez and Urs Schreiber, Higher gauge theory, to appear in the volume honoring Ross Street's 60th birthday, available as arXiv:math.DG/0511710.

  19. Toby Bartels, Higher Gauge Theory I: 2-bundles, available as arXiv:math.CT/0410328.

  20. John Baez, Alissa Crans and Danny Stevenson, Chicago lectures on higher gauge theory, available at http://math.ucr.edu/home/baez/namboodiri/

  21. John Baez, Higher gauge theory, 2006 Barrett lectures, available at http://math.ucr.edu/home/baez/barrett/

  22. John Baez, Higher-dimensional algebra: a language for quantum spacetime, colloquium talk at Perimeter Institute, available at http://math.ucr.edu/home/baez/quantum_spacetime/

  23. Sarma, Freedman, and Nayak, Topological quantum computation, Physics Today (July 2006).

  24. Topological quantum computing at Indiana University, http://www.tqc.iu.edu/

  25. Michael Freedman, Michael Larsen, and Zhenghan Wang, A modular functor which is universal for quantum computation, available as quant-ph/0001108.

  26. Parsa Bonderson, Alexei Kitaev and Kirill Shtengel, Detecting non-abelian statistics in the ν = 5/2 fractional quantum Hall state, Phys. Rev. Lett. 96 (2006) 016803. Also available as cond-mat/0508616.

  27. Charles Day, Devices based on the fractional quantum Hall effect may fulfill the promise of quantum computing, Physics Today (October 2005), also available at http://www.physicstoday.org/vol-58/iss-10/p21.html

  28. K. Eric Drexler, Nanosystems: Molecular Machinery, Manufacturing, and Computation, John Wiley and Sons, New York, 1992.

  29. Ralph C. Merkle, Two types of mechanical reversible logic, Nanotechnology 4 (1993), 114-131. Also available at http://www.zyvex.com/nanotech/mechano.html

week236

  1. National Curve Bank, Goodstein's theorem, http://curvebank.calstatela.edu/goodstein/goodstein.htm

  2. Rudy Rucker, Infinity and the Mind: The Science and Philosophy of the Infinite, Princeton University Press, Princeton, 2004.

  3. Wikipedia, Ordinal numbers, http://en.wikipedia.org/wiki/Ordinal_number

    Ordinal arithmetic, http://en.wikipedia.org/wiki/Ordinal_arithmetic

    Large countable ordinals, http://en.wikipedia.org/wiki/Large_countable_ordinals

  4. Gerhard Gentzen, Die Widerspruchfreiheit der reinen Zahlentheorie, Mathematische Annalen 112 (1936), 493-565. Translated as "The consistency of arithmetic" in M. E. Szabo ed., The Collected Works of Gerhard Gentzen, North-Holland, Amsterdam, 1969.

  5. R. Goodstein, On the restricted ordinal theorem, Journal of Symbolic Logic, 9 (1944), 33-41.

  6. L. Kirby and J. Paris, Accessible independence results for Peano arithmetic, Bull. London. Math. Soc. 14 (1982), 285-93.

  7. Alan M. Turing, Systems of logic defined by ordinals, Proc. London Math. Soc., Series 2, 45 (1939), 161-228.

  8. Jeremy Avigad and Erich H. Reck, "Clarifying the nature of the infinite": the development of metamathematics and proof theory, Carnegie-Mellon Technical Report CMU-PHIL-120, 2001. Also available as http://www.andrew.cmu.edu/user/avigad/Papers/infinite.pdf

  9. Solomon Feferman, Highlights in proof theory, in Proof Theory, eds. V. F. Hendricks et al, Kluwer, Dordrecht (2000), pp. 11-31. Also available at http://math.stanford.edu/~feferman/papers.html

  10. Solomon Feferman, Proof theory since 1960, prepared for the Encyclopedia of Philosophy Supplement, Macmillan Publishing Co., New York. Also available at http://math.stanford.edu/~feferman/papers.html

  11. Jean-Yves Girard, Y. Lafont and P. Taylor, Proofs and Types, Cambridge Tracts in Theoretical Computer Science 7, Cambridge U. Press, 1989. Also available at http://www.cs.man.ac.uk/~pt/stable/Proofs+Types.html

  12. Torkel Franzen, Inexhaustibility: A Non-Exhaustive Treatment, Lecture Notes in Logic 16, A. K. Peters, Ltd., 2004.

  13. Benno Artmann, About the cover: the mathematical conquest of the third dimension, Bulletin of the AMS, 43 (2006), 231-235. Also available at http://www.ams.org/bull/2006-43-02/S0273-0979-06-01111-6/

  14. Euclid, Elements, Book XIII, Proposition 16, online version due to David Joyce at http://aleph0.clarku.edu/~djoyce/java/elements/bookXIII/propXIII16.html

  15. Euclid, Elements, Book XIII, Proposition 18, online version due to David Joyce at http://aleph0.clarku.edu/~djoyce/java/elements/bookXIII/propXIII18.html

  16. Bill Casselman, One of the oldest extant diagrams from Euclid, http://www.math.ubc.ca/~cass/Euclid/papyrus/

  17. Thomas L. Heath, editor, Euclid's Elements, chap. V: the text, Cambridge U. Press, Cambridge, 1925. Also available at http://www.perseus.tufts.edu/cgi-bin/ptext?lookup=Euc.+5

  18. Menso Folkerts, Euclid's Elements in Medieval Europe, http://www.math.ubc.ca/~cass/Euclid/folkerts/folkerts.html

  19. Thomas L. Heath, editor, Euclid's Elements, chap. VI: the scholia, Cambridge U. Press, Cambridge, 1925. Also available at http://www.perseus.tufts.edu/cgi-bin/ptext?lookup=Euc.+6

  20. Benno Artmann, Antike Darstellungen des Ikosaeders, Mitt. DMV 13 (2005), 45-50. (Here the drawing of the icosahedron in Euclid's elements is analysed in detail.)

  21. A. E. Taylor, Plato: the Man and His Work, Dover Books, New York, 2001, page 322. (This discusses traditions concerning Theaetetus and Platonic solids.)

  22. Euclid, Elementa: Libri XI-XIII cum appendicibus, postscript by Johan Ludvig Heiberg, edited by Euangelos S. Stamatis, Teubner BSB, Leipzig, 1969. (Apparently this contains information on the scholium in book XIII of the Elements.)

  23. John Baez and James Dolan, From finite sets to Feynman diagrams, in Mathematics Unlimited - 2001 and Beyond, vol. 1, eds. Björn Engquist and Wilfried Schmid, Springer, Berlin, 2001, pp. 29-50.

  24. John Baez and Derek Wise, Quantization and Categorification, Quantum Gravity Seminar lecture notes, available at: http://math.ucr.edu/home/baez/qg-fall2003/ http://math.ucr.edu/home/baez/qg-winter2004/ http://math.ucr.edu/home/baez/qg-spring2004/

  25. Simon Byrne, On Groupoids and Stuff, honors thesis, Macquarie University, 2005, available at http://www.maths.mq.edu.au/~street/ByrneHons.pdf and http://math.ucr.edu/home/baez/qg-spring2004/ByrneHons.pdf

  26. Jeffrey Morton, Categorified algebra and quantum mechanics, Theory and Application of Categories 16 (2006), 785-854. Available at http://www.emis.de/journals/TAC/volumes/16/29/16-29abs.html; also available as arXiv:math.QA/0601458.

  27. Justin T. Miller, On the Independence of Goodstein's Theorem, Masters thesis, University of Arizona, 2001. Also available as http://www.u.arizona.edu/~miller/thesis/thesis.html

  28. Hilbert Levitz, Transfinite ordinals and their notations: For the uninitiated, available at http://www.cs.fsu.edu/~levitz/research.html

  29. Kurt Schütte, Kennzeichnung von Orgnungszahlen durch rekursiv erklärte Funktionen, Math. Ann 127 (1954), 15-32.

  30. Anton Setzer, An introduction to well-ordering proofs in Martin-Löf's type theory, in Twenty-Five Years of Constructive Type Theory, eds. G. Sambin and J. Smith, Clarendon Press, Oxford, 1998, pp. 245-263. Also available at http://www.cs.swan.ac.uk/~csetzer/index.html

    Anton Setzer, Ordinal systems, in Sets and Proofs, Cambridge U. Press, Cambridge, 2011, pp. 301-331. Also available at http://www.cs.swan.ac.uk/~csetzer/index.html

  31. Jean H. Gallier, What's so special about Kruskal's theorem and the ordinal Γ0? A survey of some results in proof theory, sec. 7, A glimpse at Veblen hierarchies, Ann. Pure Appl. Logic 53 (1991), 199-260. Also available at http://www.cis.upenn.edu/~jean/gallier-old-pubs.html

  32. Larry W. Miller, Normal functions and constructive ordinal notations, J. Symb. Log. 41 (1976), 439-459.

  33. Peter Hancock, Ordinal notation systems, http://homepages.inf.ed.ac.uk/v1phanc1/ordinal-notations.html

  34. Harold Simmons, Abstracts of papers and notes, http://www.cs.man.ac.uk/~hsimmons/DOCUMENTS/papersandnotes.html

week237

  1. Greg Egan, Klein's quartic equation, http://gregegan.customer.netspace.net.au/SCIENCE/KleinQuartic/KleinQuarticEq.html

  2. Yu. I. Manin and A. A. Panchishkin, Introduction to Modern Number Theory, second edition, Science Press, 2005.

  3. Urs Schreiber, Castellani on free differential algebras in supergravity: gauge 3-group of M-theory, http://golem.ph.utexas.edu/string/archives/000840.html

  4. Alan L. Carey, Stuart Johnson and Michael K. Murray, Holonomy on D-branes, available as arXiv:hep-th/0204199.

  5. Emanuel Diaconescu, Gregory Moore and Edward Witten, E8 gauge theory, and a derivation of K-theory from M-theory, Adv. Theor. Math. Phys. 6 (2003) 1031-1134. Also available as arXiv:hep-th/0005090.

  6. Emanuel Diaconescu, Daniel S. Freed and Gregory Moore, The M-theory 3-form and E8 gauge theory, available as arXiv:hep-th/0312069.

  7. Paolo Aschieri and Branislav Jurco, Gerbes, M5-brane anomalies and E8 gauge theory, JHEP 0410 (2004), 068. Also available as arXiv:hep-th/0409200.

  8. Leonardo Castellani, Lie derivatives along antisymmetric tensors, and the M-theory superalgebra, available as arXiv:hep-th/0508213.

  9. Pietro Fré and Pietro Antonio Grassi, Pure spinors, free differential algebras, and the supermembrane, available as arXiv:hep-th/0606171.

  10. Higher-dimensional algebra V: 2-Groups, with Aaron D. Lauda, Theory and Applications of Categories 12 (2004), available at http://www.tac.mta.ca/tac/volumes/12/14/12-14abs.html   Also available as arXiv:math.QA/0307200.

  11. Higher-dimensional algebra VI: Lie 2-Algebras, with Alissa Crans, Theory and Applications of Categories 12 (2004), available at http://www.tac.mta.ca/tac/volumes/12/15/12-15abs.html   Also available as arXiv:math.QA/0307263.

  12. Martin Markl, Steve Schnider and Jim Stasheff, Operads in Algebra, Topology and Physics, AMS, Providence, Rhode Island, 2002.

    James Stasheff, Hartford/Luminy talks on operads, available at http://www.math.unc.edu/Faculty/jds/operadchik.ps

week238

  1. NASA, NASA Announces Dark Matter Discovery, http://www.nasa.gov/home/hqnews/2006/aug/HQ_M06128_dark_matter.html

  2. Maxim Markevitch, Scott Randall, Douglas Clowe, and Anthony H. Gonzalez, Insights on physics of gas and dark matter from cluster mergers, available at http://cxc.harvard.edu/symposium_2005/proceedings/theme_energy.html#abs23

  3. M. Markevitch, S. Randall, D. Clowe, A. Gonzalez, and M. Bradac, Dark matter and the Bullet Cluster, available at http://www.cosis.net/abstracts/COSPAR2006/02655/COSPAR2006-A-02655.pdf

  4. M. Markevitch, A. H. Gonzalez, D. Clowe, A. Vikhlinin, L. David, W. Forman, C. Jones, S. Murray, and W. Tucker, Direct constraints on the dark matter self-interaction cross-section from the merging galaxy cluster 1E0657-56, available as arXiv:astro-ph/0309303.

  5. Maxim Markevitch, Chandra observation of the most interesting cluster in the Universe, available as arXiv:astro-ph/0511345.

  6. M. Markevitch, A. H. Gonzalez, L. David, A. Vikhlinin, S. Murray, W. Forman, C. Jones and W. Tucker, A textbook example of a bow shock in the merging galaxy cluster 1E0657-56, Astrophys. J. 567 (2002), L27. Also available as arXiv:astro-ph/0110468.

  7. Eric Hayashi and Simon D. M. White, How rare is the Bullet Cluster?, Mon. Not. Roy. Astron. Soc. Lett. 370 (2006), L38-L41, available as arXiv:astro-ph/0604443.

  8. PPARC, New evidence for a dark matter galaxy, http://www.interactions.org/cms/?pid=1023641

  9. Dan Christensen and Igor Khavkine, Plots of q-deformed tets, http://jdc.math.uwo.ca/spinnet/

  10. Jiri Adamek, Horst Herrlich and George E. Strecker, Abstract and Concrete Categories: the Joy of Cats, available at http://katmat.math.uni-bremen.de/acc/acc.pdf

  11. Robert Goldblatt, Topoi: the Categorial Analysis of Logic, available at http://cdl.library.cornell.edu/cgi-bin/cul.math/docviewer?did=Gold010

  12. Michael Barr and Charles Wells, Toposes, Triples and Theories, available at http://www.case.edu/artsci/math/wells/pub/ttt.html

  13. Anders Kock, Synthetic Differential Geometry, available at http://home.imf.au.dk/kock/

  14. Wikipedia, Maurer-Cartan form, http://en.wikipedia.org/wiki/Maurer-Cartan_form

  15. Victor Ginzburg and Mikhail Kapranov, Koszul duality for quadratic operads, Duke Math. J. 76 (1994), 203-272. Also Erratum, Duke Math. J. 80 (1995), 293.

  16. Benoit Fresse, Koszul duality of operads and homology of partition posets, Homotopy theory and its applications (Evanston, 2002), Contemp. Math. 346 (2004), 115-215. Also available at http://math.univ-lille1.fr/~fresse/PartitionHomology.html

week239

  1. The n-Category Café, http://golem.ph.utexas.edu/category

  2. Jacques Distler, Musings, http://golem.ph.utexas.edu/~distler/blog/

  3. Topology board of editors, letter of resignation, http://math.ucr.edu/home/baez/topology-letter.pdf

  4. Open Access News, Journal declarations of independence, http://www.earlham.edu/%7Epeters/fos/lists.htm#declarations

  5. Freeman J. Dyson, 1951 Lectures on Advanced Quantum Mechanics, second edition, available as quant-ph/0608140. For historical context and original mimeographs, see http://hrst.mit.edu/hrs/renormalization/dyson51-intro/

  6. James Gleick, Genius: the Life and Science of Richard Feynman, Vintage Press, 1993.

  7. Jagdish Mehra, The Beat of a Different Drum: the Life and Science of Richard Feynman, Oxford U. Press, 1996.

  8. Silvan S. Schweber, QED and the Men Who Made It, Princeton U. Press, Princeton, 1994.

  9. Richard P. Feynman, Surely You're Joking, Mr. Feynman! (Adventures of a Curious Character), W. W. Norton and Company, New York, 1997.

  10. Richard P. Feynman, What Do You Care What Other People Think? (Further Adventures of a Curious Character), W. W. Norton and Company, New York, 2001.

  11. Duncan J. Melville, Tokens: the origin of mathematics, from his website Mesopotamian Mathematics, http://it.stlawu.edu/%7Edmelvill/mesomath/

  12. The Schøyen Collection, MS 5067/1-8, Neolithic plain counting tokens possibly representing 1 measure of grain, 1 animal and 1 man or 1 day's labour, respectively, http://www.nb.no/baser/schoyen/5/5.11/index.html

  13. Denise Schmandt-Besserat, Accounting with tokens in the ancient Near East, http://www.utexas.edu/cola/centers/lrc/numerals/dsb/dsb.html

  14. Denise Schmandt-Besserat, Publications, http://www.utexas.edu/cola/centers/lrc/iedocctr/ie-pubs/dsb-pubs.html

  15. Eleanor Robson, Bibliography of Mesopotamian mathematics, http://it.stlawu.edu/~dmelvill/mesomath/erbiblio.html

  16. John Heise, Cuneiform writing system, http://xoomer.alice.it/bxpoma/akkadeng/cuneiform.htm

  17. Martin Markl, Steve Schnider and Jim Stasheff, Operads in Algebra, Topology and Physics, AMS, Providence, Rhode Island, 2002.

  18. Urs Schreiber, Castellani on free differential algebras in supergravity: gauge 3-group of M-theory, http://golem.ph.utexas.edu/string/archives/000840.html

  19. Urs Schreiber, SuGra 3-connection reloaded, http://golem.ph.utexas.edu/category/2006/08/sugra_3connection_reloaded.html

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Behind it all is surely an idea so simple, so beautiful, that when we grasp it - in a decade, a century, or a millennium - we will all say to each other, how could it have been otherwise? How could we have been so stupid for so long? - John Archibald Wheeler

© 2009 John Baez
baez@math.removethis.ucr.andthis.edu

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