**May 2nd, 2024 - at 17:15 in Y03 G85 **

**Sphere Packings and Magical Functions.**

**A talk in pictures on the Fields medal work of Maryna Viazovska. lecture given by ****Prof. Claire Burrin (UZH)**

Abstract :

What is the most space-efficient way to stack oranges (of same size)? The answer seems clear: stack them in a pyramid just as is done at the fruit stand. But often in mathematics, the gulf between intuition and proof is large. The sphere packing problem (or Kepler conjecture) remained one of geometry's tantalizing problems for nearly 400 years, until the computer-assisted proof of Thomas Hales in 1998 (complemented by a formal, i.e., computer-checkable, proof in 2017). Still, the more general problem of packing spheres in n-dimensional space is very poorly understood. Then in 2016 came a breakthrough; Ukrainian mathematician Maryna Viazovska announced having solved the sphere packing problem in dimension 8, and soon after (in collaboration with Cohn, Kumar, Miller, and Radchenko) in

dimension 24. For this work, she became the second woman in history to be awarded the Fields medal in 2022. At the hand of many pictures (and some formulas), I will describe the history of the sphere packing problem, the role computers have occupied in it, and some of the wondrous geometric insights leading to Viazovska’s solution. This talk will be accessible to all Bachelor students.

## Attached document

Winterthurerstrasse 190

Institut für Mathematik, Universität Zürich

8057 Zürich

Switzerland