Speaker: Professor Luca Candelori, Wayne State University Department of Mathematics

Title: Topological Hecke Operators

Abstract: We briefly review the theory of Hecke operators on classical modular forms, we give an overview of the main open questions in the subject and introduce some of the classical tools to tackle them, such as l-adic Galois representations. We then introduce Baker’s topological Hecke operators acting on elliptic homology, and attempt to analyze the structure of elliptic homology as a Hecke module in a few instances. We analyze in some detail the example of a wedge of spheres and the cofiber of alpha1. In the latter case, we re-discover some interesting congruences between modular forms of weight k and weight  k + p -1, for p prime. This is all joint work with Andrew Salch.