Topology Seminar

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

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.
Date: Thursday, April 01, 2010
Time: 4:10pm
Where: Lunt 104
Contact Person: Prof. Paul Goerss
Contact email: pgoerss@math.northwestern.edu
Contact Phone: 847-491-8544
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