Speaker: Jacob Lurie from Harvard University

Title: The Siegel Mass Formula and Weil's Conjecture (Ordway Lecture I)

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 how it can be deduced from a conjecture of Weil (now a theorem of Kottwitz, building on earlier work of Lai and Langlands) on volumes of adelic points of algebraic groups.