Here's a list of forthcoming talks... and some other stuff I plan to do. You can also see transparencies and/or videos of talks I've given, and a more detailed description of my earlier travels and talks.
On Monday a little after 10:30 am, I'll give this talk:
Network Theory
Nature and the world of human technology are full of networks. People like to draw diagrams of networks: flow charts, electrical circuit diagrams, signal-flow graphs, Bayesian networks, Feynman diagrams and the like. Mathematically minded people know that in principle these diagrams fit into a common framework. But we are still far from a unified theory of networks. Here we propose compact categories as a general framework - or for a more detailed treatment, compact bicategories. We illustrate this with a number of key examples, and show how these examples are connected by functors.
I'll give the opening talk at 9 am on Sunday June 28th:
I'll give a second talk at 2:30 on Monday June 29th:Categories in Control
Control theory is the branch of engineering that studies dynamical systems with inputs and outputs, and seeks to stabilize these using feedback. Control theory uses "signal-flow diagrams" to describe processes where real-valued functions of time are added, multiplied by scalars, differentiated and integrated, duplicated and deleted. In fact, these are string diagrams for the symmetric monoidal category of finite-dimensional vector spaces, but where the monoidal structure is direct sum rather than the usual tensor product. Jason Erbele has given a presentation for this symmetric monoidal category, which amounts to saying that it is the PROP for bicommutative bimonoids with some extra structure.A broader class of signal-flow diagrams also includes "caps" and "cups" to model feedback. This amounts to working with a larger symmetric monoidal category where objects are still finite-dimensional vector spaces but the morphisms are linear relations. Erbele also found a presentation for this larger symmetric monoidal category. It is the PROP for a remarkable thing: roughly speaking, an object with two special commutative dagger-Frobenius structures, such that the multiplication and unit of either one and the comultiplication and counit of the other fit together to form a bimonoid.
Circuits, Categories and Rewrite Rules
We describe a category where a morphism is an electrical circuit made of resistors, inductors and capacitors, with marked input and output terminals. In this category we compose morphisms by attaching the outputs of one circuit to the inputs of another. There is a functor called the "black box functor" that takes a circuit, forgets its internal structure, and remembers only its external behavior. Two circuits have the same external behavior if and only if they impose same relation between currents and potentials at their terminals. This is a linear relation, so the black box functor goes from the category of circuits to the category of finite-dimensional vector spaces and linear relations. Constructing this functor makes use of Brendan Fong's theory of "decorated cospans" — and the question of whether two circuits map to the same relation has an interesting answer in terms of rewrite rules.
Probabilities versus Amplitudes
Some ideas from quantum theory are just beginning to percolate back to classical probability theory. For example, the master equation for a chemical reaction network describes the interactions of molecules in a stochastic rather than quantum way. If we look at it from the perspective of quantum theory, this formalism turns out to involve creation and annihilation operators, coherent states and other well-known ideas — but with a few big differences.
"Scattering for Classical Yang-Mills Fields," Conference on the Construction of Quantized Gauge Fields, Cornell University, May 1988.
"Conformally Invariant Nonlinear Wave Equations," Partial Differential Equations Seminar, Brown University, October 1988.
"Scattering in Nonlinear Classical Field Theories," Theoretical Physics Seminar, Yale University, October 1988.
"Completely Integrable Field Theories in Four Dimensions," University of California, Irvine, May 1989.
"Schwinger Terms and Bosonization," Massachusetts Institute of Technology, July 1989.
"Completely Integrable Field Theories in Four Dimensions," Seminaire de Physique des Particules, Universite de Geneve, September 1989.
"Wilson Loops in Two-dimensional Yang-Mills Theory," Southern California Seminar on Witten Theory, Pomona College, May 1990.
"The Hyperbolic Yang-Mills Equations," Caltech Gauge Theory/Topology Conference, May 1990.
"Semiclassical Estimates Through Functional Integration," Massachusetts Institute of Technology, October 1990.
"Braided Geometry," Harvard University, February 1992.
"Quantum Gravity and the Algebra of Tangles," Syracuse University, July 1992.
"Quantum Gravity and the Algebra of Tangles," University of Utah, November 1992.
"Link Invariants, Holonomy Algebras and Functional Integration," University of California at San Diego, January 1993.
"Quantum Gravity and the Algebra of Tangles," Pacific Coast Gravity Meeting, U. C. Santa Barbara, March 1993.
"Link Invariants, Holonomy Algebras and Functional Integration," Concordia University, March 1993.
"Tangles, Categories, and Quantum Gravity," McGill University, March 1993.
"Diffeomorphism-invariant generalized measures on the space of connections modulo gauge transformations," Conference on Quantum Topology, Kansas State University, March 1993.
"Strings, Loops, Knots and Gauge Fields," Center for Gravitational Physics and Geometry, Pennsylvania State University, September 1993.
"Higher Algebraic Structures in Gauge Theory," Knot Theory, Low-Dimensional Topology and Quantum Groups Conference, University of Southern Alabama, February 1994.
"Knots and Quantum Gravity," Georgia Institute of Technology, March 1994.
"Higher Algebraic Structures in Gauge Theory," American Mathematical Society Meeting, Kansas State University, March 1994.
"Knots and Quantum Gravity: Progress and Prospects," Seventh Marcel Grossman Meeting on General Relativity, July 1994.
"Higher-dimensional Algebra and Topological Quantum Field Theories," Center for Gravitational Physics and Geometry, Pennsylvania State University, September 1994.
"Higher-dimensional Algebra," Mathematics Department, University of Ottawa, October 1994.
"Higher-dimensional Category Theory and Physics," Lambda Calculus Jumelage, University of Ottawa, October 1994.
"Higher-dimensional Algebra," Mathematics Department, University of Illinois at Champaign, November 1994.
"Knots and Quantum Gravity," Physics Department, University of California at Davis, December 1994.
"Spin Networks in Nonperturbative Quantum Gravity," AMS Short Course, San Francisco, January 1995.
"Spin Networks in Gauge Theory" and "Knots and Quantum Gravity," Universidad Autonoma Metropolitana, Iztapalapa, Mexico, January 1995.
"Higher-dimensional Algebra and Topological Quantum Field Theory," Mathematics Department, University of Munich, 1-month lecture series, February 1995.
"Knots and Quantum Gravity, Spin Networks in Gauge Theory," and "Higher-dimensional Algebra," Physics and Mathematics Departments, University of Milan, March 1995.
"Higher-dimensional Algebra and Topological Quantum Field Theory," ICTP, Trieste, March 1995.
"Higher-dimensional Algebra and Topological Quantum Field Theory," Department of Mathematics, University of Wales, Bangor, April 1995.
"Gauge-invariance and Diffeomorphism-invariance in Canonical Quantum Gravity," Workshop on Canonical and Quantum Gravity, Stephan Banach International Mathematical Center, Warsaw, May 1995.
"Spin Networks in Gauge Theory," Department of Physics, University of Nottingham, June 1995.
"Higher-dimensional Algebra and Topological Quantum Field Theory" (3 lectures) and "Spin Networks in Gauge Theory," IVth Oporto Meeting on Knot Theory and Physics, Portugal, June 1995.
"Spin Networks in Gauge Theory," Department of Physics, Imperial College, London, July 1995.
"Higher-dimensional Algebra and Topological Quantum Field Theory" and "Generalizing the Quantum Double Construction," Department of Mathematics, University of Arizona, October 1995.
"n-Categories in Logic, Topology and Physics," workshop on New Connections between Mathematics and Computer Science, Isaac Newton Institute, Cambridge, November 1995.
"Quantum Gravity and BF Theory in Four Dimensions," Department of Physics, U. C. Santa Barbara, December 1995.
"What is Quantum Gravity?" Sacramento Area Physics and Astronomy Colloquium, February 1996.
"A Brief History of Knots," Department of Mathematics, California State University, Fullerton, February 1996.
"Higher-dimensional Algebra and Physics," Department of Mathematics, California State University, San Bernardino, March 1996.
"Four-dimensional Algebra, Topology and Geometry," Department of Mathematics, and "Quantum Gravity and BF Theory in Four Dimensions," Center for Gravitational Physics and Geometry, Pennsylvania State University, March 1996.
"Quantum Gravity and BF Theory in Four Dimensions," 11th Geometry Festival, University of Maryland, April 1996.
"Topological Quantum Field Theory" and "Entropy of 2-Part Systems," Mathematical Problems of Quantum Gravity workshop, Erwin Schroedinger Institute, Vienna, July 1996.
"The Ladder of Dimensions," Bard College, September 1996.
"The Ladder of Dimensions," Pomona College, October 1996.
"n-Categories in Topology and Physics", Department of Mathematics, and "Spacetime Aspects of the Loop Representation of Quantum Gravity" (2 lectures), Center for Gravitational Physics and Geometry, Pennsyvlania State University, February 1997.
"Weak n-Categories", Workshop on Higher Category Theory and Physics, Northwestern University, March 1997.
"Spin Foam Models" (3 lectures), Workshop on Canonical and Quantum Gravity II, Stephan Banach International Mathematical Center, Warsaw, May 1997.
"An Algebraic Approach to Discrete Mechanics", Center for Computational Science Center, Boston University, August 1997.
"An Algebraic Approach to Discrete Mechanics", Physics of Computation Seminar, Massachusetts Institute of Technology, August 1997.
"An Introduction to n-Categories", 7th Conference on Category Theory and Computer Science, Santa Margherita Ligure, September 1997.
"Higher-dimensional Algebra and Quantum Gravity", University of California, Santa Cruz, October 1997.
"Higher-dimensional Algebra and Quantum Gravity", California State University, San Bernardino, November 1997.
"Higher-dimensional Algebra and Quantum Gravity", University of California, Irvine, November 1997.
"2-Tangles", SUNY Stony Brook, January 1998.
"Higher-dimensional Algebra and Quantum Gravity", CUNY Graduate School and University Center, January 1998.
"Spin Networks in Gauge Theory", CUNY Graduate School and University Center, March 1998.
"Higher-dimensional Algebra and Quantum Gravity", University of Memphis, March 1998.
"Spin Foam Models of Quantum Gravity" (2 lectures), Center for Gravitational Physics and Geometry, Pennsylvania State University, April 1998.
"Higher-Dimensional Knot Theory", Johns Hopkins University, May 1998.
"Higher-Dimensional Knot Theory", University of Chicago, May 1998.
"Spin Foam Models of Quantum Gravity", Enrico Fermi Institute, University of Chicago, May 1998.
"Spin Foam Models of Quantum Gravity" (3 lectures), VIIth Oporto Meeting on Geometry, Topology and Physics, Portugal, June 1998.
"Quantum Geometry and Black Hole Entropy", University of Arizona, Tucson, October 1998.
"Spin Foam Models of Quantum Gravity" (3 lectures), 38th International School of Nuclear and Particle Physics, Schladming, Austria, January 1999.
"Quantum Geometry and Black Hole Entropy", California State Polytechnic University, Pomona, March 1999.
"Quantum Geometry and Black Hole Entropy", Institute of Theoretical Physics, University of California, Santa Barbara, April 1999.
"Spin Networks, Spin Foams, and Quantum Gravity", Minnowbrook Symposium on Space-Time Structure, Syracuse University, May 1999.
"Higher-dimensional Algebra and Planck-Scale Physics", Toward a New Understanding of Space, Time, and Matter, conference at the University of British Columbia, Vancouver, June 1999.
"Spin Networks, Spin Foams, and Quantum Geometry", Conference on Physics of Strong Gravitational Fields, Institute of Theoretical Physics, University of California, Santa Barbara, June 1999.
"n-Categories" (7 hours of lectures), School on Category Theory and Applications, University of Coimbra, Portugal, July 1999.
"n-Categorical Physics", Category Theory 99, University of Coimbra, Portugal, July 1999.
"The Quantum Tetrahedron in 3 and 4 Dimensions," Instituto Superior Tecnico, Lisbon, July 1999.
"The Geometric Quantization of Geometry," Stanford University, November 1999.
"Simplicial Quantum Geometry," CUNY Graduate School and University Center, March 2000.
"From Finite Sets to Feynman Diagrams," University of Memphis, April 2000.
"Quantum Geometry and Black Hole Entropy", 13th International Congress on Mathematical Physics, Imperial College, London, July 2000.
"n-Categorical Physics", Department of Physics, University of California, Santa Barbara, October 2000.
"n-Categorical Physics", American Mathematical Society Meeting, San Francisco State University, October 2000.
"Spin Networks, Spin Foams and Quantum Gravity", Department of Physics, University of Wisconsin, Milwaukee, February 2001.
"The Meaning of Relativity", Departments of Mathematics and Physics, University of Wisconsin, Milwaukee, February 2001.
"Spin Networks in Canonical Quantum Gravity" and "The Quantum Tetrahedron", Department of Mathematics, Pennsylvania State University, March 2001.
"Lorentzian Spin Networks," Center for Gravitational Physics and Geometry, Pennsylvania State University, March 2001.
"The Meaning of Einstein's Equation," Physics Department, University of Texas at Brownsville, April 2001.
"Real Numbers, Complex Numbers, Quaternions and Octonions", Mathematics Department, California State San Bernardino, May 2001.
"New Developments in Canonical Quantum Gravity", plenary talk, 9th Canadian Conference on General Relativity and Relativistic Astrophysics, Edmonton, Canada, May 2001.
"Discrete Riemannian Geometry and Gauge Theory" (4 lectures), Graphs and Patterns in Mathematics and Theoretical Physics, a conference at SUNY Stony Brook in honor of Dennis Sullivan's 60th birthday, June 2001.
"Categorification and Computation", Conference on Algebraic Topological Methods in Computer Science, Stanford University, July 2001.
"Normed Division Algebras: A Categorical Perspective", Category Theory Seminar, Department of Pure Mathematics and Mathematical Statistics, Cambridge University, August 2001.
"Spin Foam Models of Quantum Gravity", conference on Discrete Random Geometries and Quantum Gravity, Spinoza Institute, Utrecht, October 2001.
"n-Categories in Algebraic Topology", Algebraic Topology Seminar, Mathematics Department, University of Chicago, March 2002.
"The World of n-Categories", Mathematics Department, University of Chicago, March 2002.
"Quantum Riemannian Geometry and Gauge Theory" (6 hours of lectures), Korea Institute of Advanced Studies, Seoul, March 2002.
"The World of n-Categories", Mathematics Department, University of California, Santa Cruz, April 2002.
"n-Categories in Homology Theory", Workshop on Nonabelian Hodge Theory and Higher Categories, Mathematical Sciences Research Institute, April 2002.
"Categorified Gauge Theory," Joint Meeting of the Pacific Northwest Geometry Seminar and Cascade Topology Seminar, University of Washington, Seattle, May, 2002.
"n-Categories and Homotopy Theory" (5 lectures), Department of Pure Mathematics and Mathematical Statistics, Cambridge University, July, 2002.
"The Vector Cross Product in Dimensions 0, 1, 3 and 7", Department of Mathematics, George Washington University, September 2002.
"Building Spacetime from Spin", Dirac Centenary Conference, Baylor University, Texas, October 2002.
"Higher-Dimensional Algebra and Quantum Gravity", Philosophy of Science Association, Milwaukee, November 2002.
"The Vector Cross Product in Dimensions 0, 1, 3 and 7", Department of Mathematics, University of California, San Diego, December 2002.
"Categorified Lie Algebras and Lie Groups", Algebra Mini-Conference, Department of Mathematics, University of New South Wales, Australia, January 2003.
"A Categorical Approach to Division Algebras", Australian Category Seminar, Department of Mathematics, Macquarie University, Australia, January 2003.
"Categorifying Quantum Mechanics" (4 lectures), Australian Category Seminar, Mathematics Department, Macquarie University and University of Sydney, Australia, February 2003.
"The Octonions", Pure Mathematics Department, University of Adelaide, Australia, February 2003.
"Lie 2-Groups and Lie 2-Algebras", Pure Mathematics Department, University of Adelaide, Australia, February 2003.
"From the Octonions to E_{8}", Mathematics Department, University of Western Ontario, London, Canada, March 2003.
"New Directions in Spin Foam Theory", Spin Foam Seminar, Perimeter Institute of Theoretical Physics, Waterloo, Canada, March 2003.
"Categorified Gauge Theory", Perimeter Institute of Theoretical Physics, Waterloo, Canada, March 2003.
"Quantum Geometry and Its Applications", plenary talk at Gravitation: a Decennial Perspective, Center of Gravitational Physics and Geometry, Pennsylvania State University, June 2003.
"Categorified Lie Groups, Lie Algebras, Bundles and Connections", plenary talk at the Workshop on Higher-Order Geometry and Categorification, Superior Tecnico, Lisbon, Portugal, July 2003.
"Struggles with the Continuum", plenary talk at the Young Researcher's Symposium of the ICMP, Instituto Superior Tecnico, Lisbon, Portugal, July 2003.
"Euler Characteristic versus Homotopy Cardinality", Fields Institute Program on Applied Homotopy Theory, University of Western Ontario, London, Ontario, September 2003.
"Categorification", Workshop on the Ramifications of Category Theory, University of Florence, Florence, Italy, November 2003.
"Spin Foam Models", Nonperturbative Quantum Gravity: Loops and Spin Foams, Centre Internationale de Recontres Mathématiques, Luminy, Marseille, May 2004.
"Why n-Categories?", "What n-Categories Should be Like", and "Space and State, Spacetime and Process", talks at n-Categories: Foundations and Applications, IMA, Minneapolis, June 2004.
"n-Categorical Physics", 4 lectures at the Department of Applied Mathematics and Theoretical Physics, Cambridge University, England, July 2004.
"Loop Quantum Gravity, Quantum Geometry and Spin Foams", plenary talk at 17th Conference of the International Society of General Relativity and Gravitation (GR-17), Dublin, Ireland, July 2004.
"The Problem of Dynamics in Quantum Gravity", plenary talk at Workshop on Quantum Gravity in the Americas, Perimeter Institute, Waterloo, Ontario, Canada, October 2004.
"Categorified Gauge Theory", Arithmetic, Geometry and Topology, a conference in honor of Larry Breen's 60th birthday, Institute Galilée, Université Paris 13, France, December 2004.
"Loop Quantum Gravity", plenary talk at the ACM-SIAM Symposium on Discrete Algorithms (SODA), Vancouver, British Columbia, January 2005.
"From Loop Groups to 2-Groups", Algebra Seminar, Mathematics Department, University of California at Irvine, May 2005.
"The Mysteries of Counting: Euler Characteristic Versus Homotopy Cardinality", public lecture at Categories in Algebra, Geometry and Mathematical Physics, a conference in honor of Ross Street's 60th birthday, Sydney, Australia, July 2005.
"Higher Gauge Theory", two talks at Categories in Algebra, Geometry and Mathematical Physics, a conference in honor of Ross Street's 60th birthday, Sydney and Canberra, Australia, July 2005.
"Higher Gauge Theory, Homotopy Theory and n-Categories", four lectures at a graduate summer school on Topics in Homotopy Theory at the Pacific Institute of Mathematical Sciences, Calgary, Canada, August 2005.
"Higher Gauge Theory: 2-Connections", plenary talk at the Union College Mathematics Conference, Union College, Schenectady, New York, December 2005.
"Universal Algebra and Diagrammatic Reasoning", nine lectures at Geometry of Computation 2006, Centre International de Recontres Mathématiques, Marseille, France, February 2006.
"Fundamental Physics: Where We Stand Today", Faculté des Sciences de Luminy, Marseille, France, February 2006.
"Loop Quantum Gravity", Physics Department of California State University, Long Beach, March 2006.
"Higher Gauge Theory, Higher Categories", three lectures, 24th annual Unni Namboodiri Lectures in Geometry and Topology, University of Chicago, April 2006.
"n-Categories and Cohomology", three talks in the Category Theory Seminar, Department of Mathematics, University of Chicago, April 2006.
"Higher Gauge Theory", three lectures, 2006 Barrett Lectures, University of Tennessee, Knoxville, April 2006.
"Higher-Dimensional Algebra: a Language for Quantum Spacetime", Perimeter Institute, Waterloo, Canada, May 2006.
"Fundamental Physics: Where We Stand Today", Department of Physics, University of Western Ontario, June 2006.
"Zooming Out in Time", Seminars on Long-Term Thinking, San Francisco, October 2006.
"Tales of the Dodecahedron", Reese Prosser Memorial Lecture, Mathematics Department, Dartmouth College, November 2006.
"Higher Gauge Theory", joint physics/mathematics colloquium, Louisiana State University, November 2006.
"Higher Gauge Theory", Mathematics Department, Stanford University, December 2006.
"The Homotopy Hypothesis", lecture at Higher Categories and Their Applications, Fields Institute, Toronto, January 2007.
"Quantum Quandaries: a Category-Theoretic Perspective", lecture at Philosophical and Formal Foundations of Modern Physics, Les Treilles, France, April 2007.
"Cartan Geometry and MacDowell-Mansouri Gravity: the Work of Derek Wise", lecture at the AstroParticule et Cosmologie (APC) group at Université Paris 7, July 2007.
"Why Mathematics is Boring", lecture at Mathematics and Narrative, Delphi, July 2007.
"Higher Gauge Theory and Elliptic Cohomology", lecture at the 2007 Abel Symposium, Oslo, August 2007.
"Higher Gauge Theory and the String Group", lecture at Poisson Geometry and Sigma Models, Erwin Schrödinger Institut, Vienna, August 2007.
"2-Hilbert Spaces", London Analysis and Probability Seminar, University College, London, September 2007.
"Higher Gauge Theory and the String Group", plenary talk, 22nd British Topology Meeting, Sheffield University, England, September 2007.
"Spans in Quantum Theory", keynote talk at Deep Beauty: Mathematical Innovation and the Search for an Underlying Intelligibility of the Quantum World, Princeton University, October 2007.
"Fundamental Physics: Where We Stand Today", James Madison University, Harrisonburg, Virgina, November 2007.
"5", Mathematics Department, George Washington University, Washington DC, May 2008.
"Groupoidification", Groupoids in Analysis and Geometry Seminar, Department of Mathematics, U. C. Berkeley, May 2008.
"5", Google, Mountain View, California, May 2008.
"Topological 2-Groups and Their Classifying Spaces", Workshop on Categorical Groups, Universitat de Barcelona, Spain, June 2008.
"Lie 2-Algebras", two lectures, Department of Algebra, University of Granada, Spain, June 2008.
"Groupoidification", invited lecture, Homotopy Theory and Higher Categories 2008, Centre de Recerca Matemàtica, Barcelona, Spain, June 2008.
"Computation and the Periodic Table", plenary talk at Algebraic Topological Methods in Computer Science 2008, University of Paris Diderot, Paris, July 2008.
"Classifying Spaces for Topological 2-Groups", talk at the Instituto Superior Tecnico, Lisbon, Portugal, July 2008.
"Groupoidification", talk at the Preuves, Programmes et Systemes group at Université Paris Diderot, Paris, July 2008.
"My Favorite Numbers", 3 talks forming the 2008 Rankin Lectures at the University of Glasgow, Scotland, September 2008.
"Classifying Spaces for Topological 2-Groups", and "Groupoidification", talks at the 2009 Joint Mathematics Meetings, Washington, D.C., January 2009.
"Lectures on Higher Gauge Theory", 3 talks at Higher Structures in Topology and Geometry II, a workshop at the Mathematisches Institut of the Georg-August-Universität Göttingen, February 2009.
"Categorification and Topology", invited talk at Categorification and Geometrisation from Representation Theory, University of Glasgow, April 2009.
"Categorification and Topology", plenary talk at Graduate Student Topology and Geometry Conference, University of Wisconsin, April 2009.
"Why Smooth Spaces?", invited talk at the Fields Institute workshop on Smooth Structures in Logic, Physics and Category Theory, University of Ottawa, May 2009.
"Computation and the Periodic Table", invited talk at the 24th Annual IEEE Symposium on Logic in Computer Science (LICS 2009), UCLA, July 2009.
"My Favorite Numbers" (3 talks), "Fundamental Physics: Where We Stand Today", and "Zooming Out in Time", lectures given as Cecil & Ida Green Honors Chair, Mathematics Department, Texas Christian University, Forth Worth, Texas, September 2009.
"Categorification in Mathematical Physics", 5-lecture course given at the 2nd School and Workshop on Quantum Gravity and Quantum Geometry, Corfu Summer Institute, Greece, September 2009.
"Who Discovered the Icosahedron?", invited talk at the History and Philosophy of Mathematics special session of the 2009 Fall Western Section Meeting of the AMS, U.C. Riverside, November 2009.
"Quantum Gravity", Southern California Reading Group in the Philosophy of Physics, U. C. Irvine, January 2010.
"8", Mathematics Department, Fullerton College, California, March 2010.
"5" and "Physics, Topology, Logic and Computation: a Rosetta Stone", Mathematics and Physics Departments, California State University, Fresno, April 2010.
"Electrical Circuits", Einstein Chair Mathematics Seminar, City University of New York, May 2010.
"Duality in Logic and Physics", Quantum Physics and Logic 10, Oxford University, May 2010.
"Energy, the Environment, and What Mathematicians Can Do", Department of Mathematics, Hong Kong University, March 2011.
"8", Institute of Mathematical Sciences, Chinese University of Hong Kong, March 2011.
"Higher Gauge Theory, Division Algebras and Superstrings," Workshop on Geometry and Lie Groups, Department of Mathematics, Hong Kong University, March 2011.
"Higher Gauge Theory, Division Algebras and Superstrings," Quantum Theory and Gravitation, ETH Zurich, June 2011.
"Operads and the Tree of Life", Combinatorics Seminar, Department of Mathematics, Université du Québec à Montréal, July 2011.
"Probabilities versus Amplitudes", invited talk, CQT Annual Symposium, Centre for Quantum Technologies, Singapore, December 2011.
"Network Theory", four lectures at Expository Quantum Lecture Series 5 at the Institute for Mathematical Research, Universiti Putra Malaysia, January 2012.
"Energy, the Environment and What We Can Do", public lecture at the Universiti Putra Malaysia, January 2012.
"Probabilities versus Amplitudes", invited talk, Coogee '12 Sydney Quantum Information Theory Workshop, Sydney, Australia, February 2012.
"Probabilities versus Amplitudes", Mathematics Department, Macquarie University, Australia, February 2012.
"Energy, the Environment and What We Can Do", Macquarie University, Australia, February 2012.
"Symmetric Monoidal Categories in Chemistry and Biology", Australian Category Seminar, Mathematics Department, Macquarie University, Australia, February 2012.
"Energy, the Environment and What We Can Do", Google, Mountain View, California, February 2012.
"The Beauty of Roots", Topology Seminar, Mathematics Department, National University of Singapore, February 2012.
"G2 and the Rolling Ball" and "Teleparallel Gravity and Higher Gauge Theory", Mathematics Department, University of Hong Kong, May 2012.
"Stochastic Petri Nets and Chemical Reactions", Preuves, Programmes et Systèmes group at Université Paris 7, June 2012.
"Diversity, Entropy and Thermodynamics", invited talk at Mathematics of Biodiversity, Centre de Recerca Matemàtica, Barcelona, July 2012.
"The Mathematics of Planet Earth", Mathematics Department, University of Southern California, October 2012.
"The Mathematics of Planet Earth", plenary talk at the 55th Annual Congress of the South African Mathematical Society, Stellenbosch University, South Africa, October 2012.
"The Mathematics of Planet Earth", Serge Lang Lecture, Mathematics Department, University of California at Berkeley, November 2012.
"The Azimuth Project: an Open-Access Educational Resource", American Geophysical Union Fall Meeting, December 2012.
"Network Theory", Econometrics Colloquium, Economics Department, University of California, Riverside, January 2013.
"The Mathematics of Planet Earth", Mathematics Institute, Warwick University, United Kingdom, January 2013.
"Bicategories and Tricategories of Spans", 94th Peripatetic Seminar on Sheaves and Logic, University of Sheffield, March 2013.
"The Mathematics of Planet Earth", public lecture, British Mathematical Colloquium, University of Sheffield, United Kingdom, March 2013.
"Spans and the Categorified Heisenberg Algebra", University of Nottingham, United Kingdom, March 2013.
"Energy and the Environment - What Physicists Can Do", colloquium, Perimeter Institute, April 2013.
"Energy and the Environment - What Physicists Can Do", Moreno Valley College, California, April 2013.
"Key Developments in Category Theory", Department of Logic and Philosophy of Science, University of California, Irvine, May 2013.
"The Foundations of Applied Mathematics", Category-Theoretic Foundations of Mathematics Workshop, University of California, Irvine, May 2013.
"Spans and the Categorified Heisenberg Algebra", 3-hour course, Lanzhou University, China, June 2013.
"Spans and the Categorified Heisenberg Algebra", Quantum Mathematics and Computation Symposium, Mathematical Institute, University of Oxford, October 2013.
"Learning to Live on a Finite Planet" TEDxCrocetta, Turin, Italy, October 2013.
"What is Climate Change?" and "What To Do About It?", invited lectures at What is Climate Change and What To Do About It?, Balsillie School of International Affairs, University of Waterloo, Canada, October 2013.
"Petri Nets, Chemistry, and Quantum Theory", Department of Computer Science, October 2013.
"The Mathematics of Planet Earth", Open University, United Kingdom, November 2013.
"Life's Struggle to Survive", SETI Institute, Mountain View, California, December 2013.
"Categories in Control", Mathematical Physics Seminar, Friedrich-Alexander-Universität Erlangen-Nürnberg, February 2014.
"Network Theory", four lectures at the Department of Computer Science, University of Oxford, February-March 2014.
"Operads and the Tree of Life", Topology Seminar, Mathematical Institute, University of Oxford, February 2014.
"The Mathematics of Planet Earth", Department of Computer Science, University of Birmingham, February 2014.
"Fock Space Techniques for Stochastic Physics", Quantum Field Theory Seminar, Institute of Mathematics, University of Oxford, March 2014.
"The Mathematics of Planet Earth", Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, March 2014.
"Network Theory", lecture as part of Category Theory at the Crossroads, Schloss Dagstuhl, Germany, May 2014.
"Operads and the Tree of Life", Topology Seminar, Université de Lille, Lille, France, May 2014.
"Operads and the Tree of Life", invited lecture, Institut Henri Poincaré, Paris, May 2014.
"Spans and the Categorified Heisenberg Algebra", Catégories, Logiques, Etc., Paris, May 2014.
"Network Theory", Computer Science Semiar, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany, May 2014.
"Biodiversity, Entropy and Thermodynamics", invited lecture at Biological and Bio-Inspired Information Theory, Banff International Resarch Station, October 2014.
"Networks in Climate Science", plenary talk at Neural Information Processing Systems 2014, Montréal, Canada, December 2014.
"Information and Entropy in Biological Systems", introductory talk at the Investigative Workshop on Information and Entropy in Biological Systems at the National Institute for Mathematical and Biological Synthesis, Knoxville, Tennessee, April 2015.
"Split octonions and the rolling ball", Geometry-Analysis-Physics Seminar, Mathematics Department, Pennsylvania State University, April 2015.
"The exceptional Jordan algebra and the Leech lattice", Geometry Luncheon Seminar, Mathematics Department, Pennsylvania State University, April 2015.
"8", University of York Mathematics Society, April 2015.