Seminar in Algebraic Geometry and Number Theory

Abstract: Counting points of a random lattice -- a random element of SL(n,Z) \ SL(n,R) with respect to its natural probability measure -- has become a popular topic in recent years. The integral formulas of Siegel and Rogers, which translate an integral of counting functions over random lattices to an integral over a Euclidean space, are essential tools for such a task. In this talk, I will discuss several known approaches to proving formulas of this kind, and introduce some recent results.