Modul: MAT760 Ergodic theory and dynamical systems seminar

## Effective Counting of Sphere Packings

Talk by Christopher Enno Hardy Lutsko

**Date:** 16.10.23 **Time:** 15.00 - 16.00 **Room:** Y27H25

In this talk I'll present a method, using abstract spectral theory, for counting points in a group orbit. That is, given a discrete group of isometries acting on the (n+1) dimensional upper half-space, our method allows one to count the number of points in an orbit a distance T from an observer. In particular, the method does not rely on an explicit pre-trace formula, and thus can be used in infinite volume. Further, I will present how to extend the method to obtain effective error rates when counting Apollonian (and more generally Kleinian) sphere packings. This is based on joint work with Alex Kontorovich, and joint work with Dubi Kelmer and Alex Kontorovich.''