Moonshine elements in elliptic cohomology

TL;DR

This paper discusses the recent convergence of research in equivariant elliptic cohomology for both connected Lie groups and finite groups, highlighting Ganter's work linking McKay-Thompson series to exponential cohomology operations.

Contribution

It reviews the emerging connection between McKay-Thompson series replicability and exponential cohomology operations in equivariant elliptic cohomology.

Findings

Ganter's work relates replicability to cohomology operations

Bridges finite and connected Lie group cases in elliptic cohomology

Highlights the historical development of these research themes

Abstract

This is a historical talk about the recent confluence of two lines of research in equivariant elliptic cohomology, one concerned with connected Lie groups, the other with the finite case. These themes come together in (what seems to me remarkable) work of N. Ganter, relating replicability of McKay-Thompson series to the theory of exponential cohomology operations.