PIMS/ UBC Distinguished Colloquium: Jacob Lurie

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 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.