What is (non-equivariant) elliptic cohomology?

Abstract: In this talk we will begin with a sketch of what elliptic cohomology is really about. Thus we will introduce the concept of a genus, which is an invariant of manifolds which are equipped with extra structure, and from there we will define an elliptic genus. We then aim to briefly describe the role of elliptic genera in elliptic cohomology, and to sketch the relationship to index theory on free loop spaces. If time permits, we will finally describe a version of elliptic cohomology which was constructed in terms of the K-theory of free loop spaces by Kitchloo and Morava.

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.