The Physics & Astronomy Colloquium Series presents Matt Ando of Ohio University, discussing "Elliptic Genera, the Witten Genus, Modularity, and the String Group" on Feburary 27.

Abstract: The Witten genus attaches to an oriented, compact smooth manifold M a rational power series w(M) in a variable q. If the manifold M admits a string structure, then w(M) has integer coefficients. Witten showed that if in addition, the first Pontryagin class of M vanishes, then w(M) is the q-expansion of a modular form. This fact raises several questions, including, what is the geometric meaning of the first Pontryagin class and its vanishing?

I’ll propose an answer in terms of a "topological field theory” on the group Spin(d).