Arnav Tripathy – Geometric Methods in Representation Theory Seminar

Title: A geometric model for complex analytic equivariant elliptic cohomology

Abstract: A long-standing question in the study of elliptic cohomology or topological modular forms has been the search for geometric cocycles. Such cocycles are crucial for applications in both geometry and, provocatively, for the elliptic frontier in representation theory. I will explain joint work with D. Berwick-Evans which turns Segal’s physically-inspired suggestions into rigorous cocycles for the case of equivariant elliptic cohomology over the complex numbers, with some focus on the role of supersymmetry on allowing for the possibility of rigorous mathematical definition. As time permits, I hope to indicate towards the end how one might naturally extend these ideas to higher genus.

This talk is joint with the Physically Inspired Mathematics Seminar