Equidistribution problem in the space of Euclidean sublattices

Abstract: Consider the space of covolume-one sublattices of a fixed rank m in the Euclidean space ℝd. How do the orbits behave under the action of the lattice subgroups of SL(d,ℝ) (e.g. SL(d,ℤ))? In a recent joint work with Michael Bersudsky, we established an equidistribution phenomenon of such orbits when d=m+1. However, there are many more unsolved problems along this direction which might be of interest not only to homogeneous dynamicists, but also to number theorists and analysts as well. In this talk, I will explain the problem, our result, an overview of methods and further directions of research in a user-friendly way.

dynamical systemsnumber theory

Audience: general audience

New England Dynamics and Number Theory Seminar