Topological modular forms and their co-operations

Paul VanKoughnett (Purdue University)

Resumen: Topological modular forms (TMF) is a cohomology theory built out of elliptic curves. I'll describe what TMF is, how it's constructed, and how it's been useful in topology, as well as some of the more speculative recent attempts to extend its construction. I'll then talk about the problem of calculating TMF co-operations, which are an essential input to serious computations using TMF. Part of this co-operations algebra -- the part that is obtained from ordinary elliptic curves -- admits a simple algebraic description, as well as an interesting relationship with number theory. This is joint work with Dominic Culver.