Harvard University

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 on volumes of adelic points of algebraic groups. This conjecture was proven for number fields by Kottwitz, building on earlier work of Langlands and Lai. I will conclude by sketching joint work (in progress) with Dennis Gaitsgory, which uses topological ideas to attack Weil's conjecture in the case of function fields.

In the Said Business School

The covariance between nominal bonds and stocks has varied considerably over recent decades and has even switched sign. It has been predominantly positive in periods such as the late 1970s and early 1980s when the economy has experienced supply shocks and the central bank has lacked credibility. It has been predominantly negative in periods such as the 2000s when investors have feared weak aggregate demand and deflation. This lecture discusses the implications of changing bond risk for the shape of the yield curve, the risk premia on bonds, and the relative pricing of nominal and inflation-indexed bonds.