Title: Tamagawa Numbers via Nonabelian Poincare Duality

Abstract:
Let L be a positive definite lattice. There are only finitely many positive definite lattices L’ which are isomorphic to L modulo N for every N > 0: in fact, there is a formula for the number of such lattices, called the Siegel mass formula. In this talk, I’ll review the Siegel mass formula and explain how it was reformulated by Tamagawa and Weil as a statement about volumes of adelic groups. I’ll then describe some joint work with Dennis Gaitsgory on computing these volumes over function fields using ideas from topology: in particular, a nonabelian version of Poincare duality.

Wednesday, February 08, 4:30 – 5:30 p.m.
Mathematics 520
Tea will be served at 4:00 p.m.

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