What is equivariant elliptic cohomology?

Abstract: Elliptic cohomology was introduced in the late 1980s following Witten's results about the index theory of families of differential operators on free loop spaces. In a certain sense it is an approximation to the K-theory of the free loop space. The first equivariant version of the theory was constructed in 1994 by Grojnowski, who made comments about its mysterious relationship to the representation theory of loop groups. In this talk, we outline a construction of equivariant elliptic cohomology whose main ingredient is the loop group equivariant K-theory of the free loop space. The construction is based on a recent construction of Kitchloo.

algebraic geometrycombinatoricsdifferential geometrynumber theoryrepresentation theory

Audience: learners

What is ...? Seminar

Series comments: The ``What is ... ? Seminar'' (WiSe) is a weekly Zoom mathematics seminar. The goal is to explain interesting things to each other in a casual manner. The name is inspired by the What is ...? column of the Notices of the American Mathematical Society. See the website for more details. If you want to receive the zoom link for the talks please fill out the form linked on the website or contact Anna at a.puskas@uq.edu.au.