|Speaker:||Alexander Voronov (U. Minnesota)|
|Title:||Higher Categories and TQFTs|
|Date:||Tue, Jun 29, 2010, 13:15 - 14:45|
The goal of the talk is to describe categorical formalism for higher dimensional, a.k.a. 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 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's. This is a joint work with Mark Feshbach.
Part 1: In the first part of the talk, I will present familiar examples of TQFTs in this setup, including gauge theory, WZW, and sigma-model.
Part 2: In the second part, I will discuss the notion of a (symmetric monoidal) pseudo n-fold category and examples thereof: the category of n-cobordisms with corners and the category of n-spans, which are the source and the target categories of a general (extended) TQFT functor.
Remarks: There will be a 5-minute break after Part 1 (30 min).