Conic optimization for extremal geometry

Abstract

The aim of this paper is to highlight recent progress in using conic optimization methods to study geometric packing problems. We will look at four geometric packing problems of different kinds: two on the unit sphere -- the kissing number problem and measurable $\ddot{I}€/2$-avoiding sets -- and two in Euclidean space -- the sphere packing problem and measurable one-avoiding sets.

25 pages, contribution to the Proceedings of the ICM 2026 (Section: Control Theory and Optimization)