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

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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

Watch the video:

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.