Algebra/Topology Seminar

Speaker: François Charles

Title: Some infinite-dimensional versions of Minkowski's theorems in the geometry of numbers

Abstract: Minkowski's celebrated theorem on lattice points in convex symmetric sets is a fundamental tool in classical geometry of numbers. The estimate it entails becomes worse and worse as the rank of the lattice grows. I will explain how the systematic use of theta functions and their infinite-dimensional avatars allows for a generalization to lattices of possibly infinite rank. Applying this theory to lattices underlying polynomial rings, I will outline applications to the geometry of integral points in affine schemes. This is joint work with Jean-Benoît Bost.