# Alexey Garber “Voronoi conjecture for five-dimensional parallelohedra” | Big Seminar

October 15, 2020
19.00 MSK (UTC +3)

# 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.

The talk will be held in zoom
Meeting ID: 279-059-822
Password: first 6 decimal places of $\pi$ after the decimal point

You can also write to Alexander Polyanskii (alexander.polyanskii@yandex.ru) or to Maksim Zhukovskii (zhukmax@gmail.com) if you want to be added to mailing list.

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.

Slides Slides with notes

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.