Title: Field theories and cohomology
Speaker: Stephan Stolz
Speaker Info: Notre Dame
Graeme Segal suggested two decades ago that the generalized cohomology theory now known as "Topological Modular Form Theory" of a manifold X should be related to families of 2-dimensional field theories parametrized by X. This is an analog of the well-known statement that homotopy classes of families of Fredholm operators parametrized by X can be identified with the K-theory of X.Date: Thursday, April 28, 2011
In this talk on joint work with Peter Teichner, I will present a conjectural picture of TMF(X) as homotopy classes of families of supersymmetric 2-dimensional Euclidean field theories parametrized by X. Evidence for the conjecture comes from an analogous description of K(X) in terms of 1-dimensional field theories, and our result that the partition function of a supersymmetric 2-dimensional Euclidean field theory is a modular form. The latter is the main focus of the talk.