Thu, November 26, 2020
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7:00pm [7:30pm] Alexey Garber
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.