Alexey Garber "Voronoi conjecture for five-dimensional parallelohedra"

Alexey Garber from The University of Texas Rio Grande Valley will give the talk "Voronoi conjecture for five-dimensional parallelohedra" on the labs' Big Seminar.

Abstract:

In this talk I am going to discuss a well-known connection between lattices in $\mathbb{R}^d$ and convex polytopes that tile $\mathbb{R}^d$ with translations only.

My main topic will be the Voronoi conjecture, a century old conjecture which is, while stated in very simple terms, is still open in general. The conjecture states that every convex polytope that tiles $\mathbb{R}^d$ with translations can be obtained as an affine image of the Voronoi domain for some lattice.

I plan to survey several known results on the Voronoi conjecture and give an insight on a recent proof of the Voronoi conjecture in the five-dimensional case. The talk is based on a joint work with Alexander Magazinov.

Everyone is invited to attend. The language of the lecture is English. The event is aimed at master and graduate students, as well as researchers in the field of combinatorics.