Lattices, Parallelohedra, and the Voronoi Conjecture.

17^th February 2026, 14:00
Alexey Garber
University of Texas Rio Grande Valley, US

Abstract

In the talk I will mostly discuss parallelohedra, the convex polytopes that tile d-dimensional Euclidean space with translations only. Study of parallelohedra goes back to Fedorov and his study of crystallographic groups in small dimensions, and Minkowski and his foundational works on lattices and geometry of numbers. My main goal will be to connect properties of these polytopes with various questions of mathematics and mathematical crystallography, and to discuss recent progress on the Voronoi conjecture.