Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Linnik's problem and statistics of orthogonal lattices of primitive integral vectors

Talk by Michael Bersudsky

**Date:** 11.10.21 **Time:** 15.00 - 16.00 **Room:** Y27H28

I will discuss my joint work with Uri Shapira in which we generalize Aka, Einsiedler and Shapira's results on the statistics of shapes of orthogonal lattices of primitive integral vectors lying on large spheres (in dimensions larger than 4). Part of my talk will explain how the result obtained by Aka, Einsiedler and Shapira can be deduced from a result that can be thought of as a variant in a non-Euclidean setting of Linnik's classical equidistribution theorem about the directions of primitive integral vectors on a large sphere.