Daniel Berwick-Evans, University of California-Berkeley
Abstract: We will explain a way in which geometric field theories can be used to study the topology of manifolds. After setting up the main players as defined by Stolz and Teichner, we'll focus attention on dimensional reduction and quantization.

The former allows us to extract numerical invariants whereas the latter can be used to produce a linear approximation (in the sense of Goodwillie calculus) that builds a cohomology theory out of a space of twisted field theories.