Student Geometry/Topology Seminar

If TQFTs had been defined first in a purely mathematical context, they might well have been called "linear cobordism representations." In reality, these objects first came to our attention in the context of physics, where they play the role of a toy model meant to give insight on quantum gravity. The Cobordism Hypothesis, proposed by Baez and Dolan and proved by Lurie, suggests that TQFTs have a natural home in the world of higher category theory. In neighboring mathematical contexts, TQFTs have been used to construct knot invariants via their role as an ingredient in Khovanov homology, and lend themselves very naturally to the construction of diffeomorphism invariants of manifolds.

In this talk, I would first like to sketch some of the background that first motivated the study of TQFTs. Then I will go into some detail in the case of 2-dimensional TQFTs, and this 2-dimensional example will give us the first glimpses of how one might come to formulate the Cobordism Hypothesis. At the end, I will try to give an indication of the ways people have used TQFTs to shed light on other mathematical questions. Speaker(s): Bradley Zykoski (University of Michigan)