I work on mathematical physics — which I interpret broadly as ‘math that could be of interest in physics, and physics that could be of interest in math’. I’m especially interested in $n$-categories and their applications. I’ve spent a lot of time explaining these subjects on the web. You can see a sampling below. For a lot more stuff, see my website.

If you visit my personal web here, you’ll see my work with James Dolan on doctrines in algebraic geometry, and the preface of a book I edited with Peter May, called *Towards Higher Categories*.

Symmetries, Groups, and Categories

Categories, Quantization and Much More

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

Higher-dimensional algebra I: braided monoidal 2-categories, with Martin Neuchl, Adv. Math. 121 (1996), 196-244.

An introduction to $n$-categories, in *7th Conference on Category Theory and Computer Science*, eds. E. Moggi and G. Rosolini, Springer Lecture Notes in Computer Science vol. 1290, Springer, Berlin, 1997.

Higher-dimensional algebra II: 2-Hilbert spaces, Adv. Math. 127 (1997), 125-189.

Higher-dimensional algebra III: $n$-categories and the algebra of opetopes, with James Dolan, Adv. Math. 135 (1998), 145-206.

Spin foam models, Class. Quantum Grav. 15 (1998), 1827-1858.

Categorification, with James Dolan, in *Higher Category Theory*, eds. Ezra Getzler and Mikhail Kapranov, Contemp. Math. 230, American Mathematical Society, Providence, Rhode Island, 1998, pp. 1-36.

An introduction to spin foam models of *BF* theory and quantum gravity, in *Geometry and Quantum Physics*, eds. Helmut Gausterer and Harald Grosse, Springer, Berlin, 2000, pp. 25-93.

From finite sets to Feynman diagrams, with James Dolan, in *Mathematics Unlimited - 2001 and Beyond*, vol. 1, eds. Björn Engquist and Wilfried Schmid, Springer, Berlin, 2001, pp. 29-50.

Higher-dimensional algebra and Planck-scale physics, in *Physics Meets Philosophy at the Planck Length*, eds. Craig Callender and Nick Huggett, Cambridge U. Press, Cambridge, 2001, pp. 177-195. Also available as a webpage.

Higher-dimensional algebra IV: 2-tangles, with Laurel Langford, Adv. Math. 180 (2003), 705-764.

Higher-dimensional algebra V: 2-groups, with Aaron D. Lauda, Theory and Applications of Categories 12 (2004), 423-491.

Higher-dimensional algebra VI: Lie 2-algebras, with Alissa S. Crans, Theory and Applications of Categories 12 (2004), 492-528.

Quantum quandaries: a category-theoretic perspective, in *Structural Foundations of Quantum Gravity*, eds. Steven French, Dean Rickles and Juha Saatsi, Oxford U. Press,Oxford, 2006, pp. 240-265. Also available as a webpage

Higher gauge theory, with Urs Schreiber, in *Categories in Algebra, Geometry and Mathematical Physics*, eds. Alexei Davydov, Michael Batanin, Michael Johnson, Stephen Lack and Amnon Neeman, Contemp. Math. 431, American Mathematical Society, Providence, Rhode Island, 2007, pp. 7-30.

From loop groups to 2-groups with Alissa S. Crans, Danny Stevenson and Urs Schreiber, Homotopy, Homology and Applications, 9 (2007), 101-135.

Lectures on $n$-categories and cohomology, with Michael Shulman, to appear in *n-Categories: Foundations and Applications*, eds. John Baez and Peter May.

The classifying space of a topological 2-group, with Danny Stevenson, to appear in the proceedings of the 2007 Abel Symposium, eds. Nils Baas *et al*.

Convenient categories of smooth spaces, with Alex Hoffnung.

Categorified symplectic geometry and the classical string, with Alex Hoffnung and Chris Rogers.

Categorified symplectic geometry and the string Lie 2-algebra, with Christopher L. Rogers.

Representations of 2-groups on higher Hilbert spaces, with Aristide Baratin, Laurent Freidel and Derek Wise.

Physics, topology, logic and computation: a Rosetta Stone, with Mike Stay, in *New structures for physics*, pp. 95-172. Springer, Berlin, Heidelberg, 2010.

Groupoidification made easy, with Alexander E. Hoffnung and Christopher D. Walker.

A history of n-categorical physics, with Aaron Lauda, in proceedings of *Deep Beauty: Mathematical Innovation and the Search for an Underlying Intelligibility of the Quantum World*, ed. Hans Halvorson.

category: people

Last revised on October 18, 2020 at 15:27:40. See the history of this page for a list of all contributions to it.