Sphere packings and automorphic forms

The densest sphere packing problem is a multi-dimensional generalization of the famous Kepler conjecture. In 2016 M. Vyazovskaya was able to completely solve the problem in dimensions 8 and 24, where densest packings correspond to E_8 lattice and Leech lattice respectively. We will discuss the proof of Vyazovskaya's result, which surprisingly uses certain properties of automorphic forms.