Description
Speaker: Alexey Garber.
Time: 7:30 pm (IST) gate opens 7:15 pm IST, 26 November, 2020
Google meet link: meet.google.com/zis-ovwc-tjy.
Title: Voronoi conjecture for five-dimensional parallelohedra.
Abstract: In this talk I am going to discuss a well-known connection
between lattices in $\mathbb{R}^d$ and convex polytopes that tile
$\mathbdd{R}^d$ 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.