Topological Quantum Field Theory.
Functional analysis on the eve of the 21st century Contains article by Kapranov: Analogies between the Langlands Correspondence and Topological QFT. Really cool article. Follow-up here at MO.
http://mathoverflow.net/questions/359/a-reading-list-for-topological-quantum-field-theory
http://nlab.mathforge.org/nlab/show/extended+topological+quantum+field+theory
nLab on the cobordism hypothesis
http://nlab.mathforge.org/nlab/show/On+the+Classification+of+Topological+Field+Theories
http://nlab.mathforge.org/nlab/show/generalized+tangle+hypothesis
Some notes by May
A blog entry of Baez
Notes by Toen on higher-categorical structures in TQFT, in Toen web unpubl folder, etqft.dvi.
Blog post on Ben-Zvi lectures on Topological field theories
Lectures on tensor cats and modular functor. Link
Explore nlab stuff on Chern-Simons theory.
arXiv:1108.3349 A higher category of cobordisms and topological quantum field theory from arXiv Front: math.CT by Mark Feshbach, Alexander A. Voronov 1 person liked this The goal of this work is to describe a categorical formalism for (Extended) Topological Quantum Field Theories (TQFTs) and present them as functors from a suitable category of cobordisms with corners to a linear category, generalizing 2d open-closed TQFTs to higher dimensions. The approach is based on the notion of an n-fold category by C. Ehresmann, weakened in the spirit of monoidal categories (associators, interchangers, Mac Lane’s pentagons and hexagons), in contrast with the simplicial (weak Kan and complete Segal) approach of Jacob Lurie. We show how different Topological Quantum Field Theories, such as gauge, Chern-Simons, Yang-Mills, WZW, Seiberg-Witten, Rozansky-Witten, and AKSZ theories, as well as sigma model, may be described as functors from the pseudo n-fold category of cobordisms to a pseudo n-fold category of sets.
nLab page on TQFT