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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. You can also see the latest edition or all old editions. To search old editions, use the box above and add "week" to your search terms.

Many of the papers I review are available on the arXiv. If you click on the number of one of these papers, such as 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 hep-th/9301028.

  3. Time, measurement and information loss in quantum cosmology, by Lee Smolin, preprint now available as 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 hep-th/9301061 in amstex.

    A Categorical construction of 4d topological quantum field theories, by Louis Crane and David Yetter, preprint available as 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 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. (Kapranov is at kapranov@chow.math.nwu.edu, and Voevodsky is at vladimir@math.ias.edu.)

week5

  1. Indecomposable restricted representations of quantum sl_2, Vyjanathi Chari and Alexander Premet, University of California at Riverside preprint.

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

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

  4. The new configuration space for gravity: the spectrum of the algebra of SL(2,C)-holonomy functionals, by Abhay Ashtekar and Jerzy Lewandowski, draft version.

week6

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

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

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 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 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 gr-qc/9302020, 15 pages.

  5. Combinatorial expression for universal Vassiliev link invariant, by Sergey Piunikhin, preprint available as 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 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 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 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 gr-qc/9303026.

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

  5. Canonical Quantum Gravity and the Problem of Time, Chris J. Isham, 125 pages, preprint available as 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 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 gr-qc/9303015.

  4. Surgical invariants of four-manifolds, by Boguslaw Broda, preprint available as 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 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 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 gr-qc/9304005.

  4. Higher algebraic structures and quantization, by Dan Freed, preprint, December 18, 1992, available as 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 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 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 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 gr-qc/9304043.

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

week15

  1. Closed string field theory - an introduction, by Barton Zwiebach, preprint available as 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 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 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 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 gr-qc/9305020.

  5. An illustration of 2+1 gravity loop transform troubles, by Donald Marolf, available as 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 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 hep-th/9305022.

  8. A note on the four-dimensional Kirby calculus, by Boguslaw Broda, preprint, 5 pages, preprint available as 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 gr-qc/9305025.

week18

  1. Strings, loops, knots, and gauge fields, by John Baez, preprint available as 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 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 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 gr-qc/9311010)

    The Gauss linking number in quantum gravity, by Rodolfo Gambini and Jorge Pullin (currently available as 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 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 hep-th/9308126)

    Strings, loops, knots and gauge gields, by John Baez (currently available as 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 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 hep-th/9310144.

  3. Semi-classical limits of simplicial quantum gravity, by J. W. Barrett and T. J. Foxon, preprint available as 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 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 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 gr-qc/9311010.

week26

  1. Cosmology, time's arrow, and that old double standard, by Huw Price, 26 pages, available as 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 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 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 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 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 gr-qc/9308002.

    Fermions in quantum gravity, by H. A. Morales-Tecotl and C. Rovelli, 37 pages, preprint available as 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 gr-qc/9312029.

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

week31

  1. Possible implications of the quantum theory of gravity, by Louis Crane, 5 pages, preprint available as 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 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 hep-th/9305040.

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

    Black hole entropy in canonical quantum gravity and superstring theory, by L. Susskind and J. Uglum, 29 pages, available as 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 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 hep-th/9308044.

  8. "No hair" theorems -- folklore, conjectures, results, by Piotr T. Chrusciel, Garching preprint MPA 792, 30 pages available as 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 hep-th/9403015.

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

  3. Gromov-Witten classes, quantum cohomology, and enumerative geometry, by M. Kontsevich, Yu. Manin, 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 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 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 hep-th/9407070.

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

  3. A Hamiltonian formulation of topological gravity, by Henri Waelbrock and J. A. Zapata, 15 pages, preprint available as 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 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 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 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 hep-th/9311155.

    The equality of 3-manifold invariants, by John W. Barrett and Bruce W. Westbury, preprint available as 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 hep-th/9406065.

  6. Four dimensional topological quantum field theory, Hopf categories, and the canonical bases, by Louis Crane and Igor Frenkel, available as 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 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 gr-qc/9406025.

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

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

    Independent loop invariants for 2+1 gravity, by R. Loll, 2 figures, 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 gr-qc/9404060.

    The extended loop representation of quantum gravity, C. Di Bartolo, R. Gambini and J. Griego, 27 pages available as 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 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 hep-th/9409044.

  3. Strings and two-dimensional QCD for finite N, by J. Baez and W. Taylor, 19 pages available as 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 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 gr-qc/9406019.

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

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

  7. "Matters of Gravity", a newsletter for the gravity community, Number 4, edited by Jorge Pullin, 24 pages, preprint available as 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 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 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 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 gr-qc/9410010.

  11. Lattice QCD as a theory of interacting surfaces, by B. Rusakov, TAUP-2204-94, 12 pages, preprint available as 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 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 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 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 hep-th/9409167.

  5. Spin networks in gauge theory, by John Baez, 19 pages, preprint available as 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 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 hep-th/9407087.

    Monopoles, duality and chiral symmetry breaking in N=2 supersymmetric QCD, by Nathan Seiberg and Edward Witten, 89 pages, available as 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 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 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 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 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 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 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 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 hep-th/9410085.

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

  13. Speedup in quantum computation is associated with attenuation of processing probability, by Karl Svozil, available as 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 q-alg/9501025.

  2. Higher algebraic structures and quantization, by Daniel Freed, Comm. Math. Phys. 159 (1994), 343-398; preprint available as 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, hep-th/9403066 and 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 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 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 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 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 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 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 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 gr-qc/9505028.

  2. G 't Hooft, Dimensional reduction in quantum gravity, preprint available as 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 hep-th/9409089.

    L. Susskind, Strings, black holes and Lorentz contractions, preprint available as 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 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 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 hep-th/9410202.

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

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

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

    Octonions: invariant Leech lattice exposed, preprint available as 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 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 gr-qc/9412035.

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

  7. John Baez, Javier P. Muniain and Dardo Piriz, Quantum gravity hamiltonian for manifolds with boundary, available as 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 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 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 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 gr-qc/9504004.

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

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

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

  8. Joseph Polchinski and Edward Witten, Evidence for Heterotic - Type I String Duality, preprint available as 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 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 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 gr-qc/9510033.

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

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

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

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

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

    The Kauffman bracket and the Jones polynomial in quantum gravity, preprint available as 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 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 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 hep-th/9506011.

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

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

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

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

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

    Rodolfo Gambini and Jorge Pullin, A rigorous solution of the quantum Einstein equations, preprint avilable in RevTex form as 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 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 q-alg/9511025.

    Scott Axelrod, Overview and warmup example for perturbation theory with instantons, preprint available as 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 hep-th/9511151.

    Alan Carey, M. K. Murray and B. L. Wang, Higher bundle gerbes and cohomology classes in gauge theories, preprint available as 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 hep-th/9511157, uses PTPTeX.sty.

  8. Leonard Susskind and John Uglum, String physics and black holes, preprint available as 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 q-alg/9511010.

  10. John Baez and Martin Neuchl, Higher-Dimensional Algebra I: Braided Monoidal 2-Categories, 51 pages, available as a compressed PostScript file at http://math.ucr.edu/home/baez/bm2cat.ps.Z

    This paper is q-alg/9511013, but looking for it there will just lead you to the above site.

week72

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

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

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

    Roumen Borissov, Seth Major and Lee Smolin, The geometry of quantum spin networks, preprint available as 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 gr-qc/9512036.

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

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

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

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

  4. Thomas Kerler, Genealogy of nonperturbative quantum-invariants of 3-manifolds: the surgical family, preprint available as 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 gr-qc/9602046.

    Jerzy Lewandowski, Volume and Quantizations, preprint available as 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 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 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 gr-qc/9603019.

week78

  1. Higher algebraic structures and quantization, by Daniel Freed, Commun. Math. Phys. 159 (1994), 343-398, also available as 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 astro-ph/9410067

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

    R. J. Protheroe and P. A. Johnson, Are topological defects responsible for the 300 EeV cosmic rays?, preprint available as 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 hep-th/9603053.

    Ali H. Chamseddine and Alain Connes, The spectral action principle, preprint available as 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 hep-th/9605018.

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

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

week85

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

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

    Thomas Thiemann, Quantum Spin Dynamics (QSD) II, preprint available as 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 gr-qc/9606088.

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

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

  3. Kirill Krasnov, Quantum loop representation for fermions coupled to Einstein-Maxwell field, Phys. Rev. D53 (1996), 1874; preprint available as 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 gr-qc/9401011.

week86

  1. Discreteness of area and volume in quantum gravity, by Carlo Rovelli and Lee Smolin, 36 pages, available as 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 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 gr-qc/9410010.

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

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

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

  5. Jerzy Lewandowski, Volume and quantizations, preprint available as 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 gr-qc/9608032.

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

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

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

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

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

  5. Hugo Fort, Rodolfo Gambini and Jorge Pullin, Lattice knot theory and quantum gravity in the loop representation, preprint available as 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 hep-th/9507020.

    Peter Schaller and Thomas Strobl, Poisson sigma-models: a generalization of 2d gravity-Yang-Mills systems, preprint available as 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 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 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 gr-qc/9609019.

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

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

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

  8. John Baez and Martin Neuchl, Higher-dimensional algebra I: braided monoidal 2-categories, 51 pages, available as a compressed PostScript file at http://math.ucr.edu/home/baez/bm2cat.ps.Z.

  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 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 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 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 hep-th/9411188

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

  9. Reinhold W. Gebert, Introduction to vertex algebras, Borcherds algebras, and the Monster Lie algebra, preprint available as 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 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 hep-th/9612090.

  3. Michael Reisenberger and Carlo Rovelli, "Sum over surfaces" form of loop quantum gravity, preprint available as 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 hep-th/9701136.

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

week98

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

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

  3. John Baez, Degenerate solutions of general relativity from topological field theory, preprint available as 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 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 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 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 gr-qc/9504038.

  8. John Baez, Higher-dimensional algebra II: 2-Hilbert spaces, to appear in Adv. Math., preprint available as 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 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.

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