EVENT DETAILS AND ABSTRACT

Title: Topological modular forms, group cohomology, and duality
Speaker: Vesna Stojanoska
Speaker Info: Northwestern University
Brief Description:
Special Note: Special Day
Abstract:

When $2$ is inverted, choice of level $2$-structure for an elliptic curve provides a geometrically well-behaved cover of the (compactified) moduli stack of elliptic curves. It allows one to consider the spectrum of topological modular forms $tmf$ as the homotopy fixed points of $tmf(2)$, topological modular forms with level $2$-structure, under a natural action of the (finite) group $GL_2(\Z/2)$. Grothendieck-Serre duality makes $tmf(2)$ self dual; combining this with the vanishing of the associated generalized Tate cohomology, we obtain that $tmf$ is Anderson self-dual. This is a geometric explanation of a duality noticed by Mahowald and Rezk.