BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexey Garber (The University of Texas Rio Grande Valley) DTSTART:20210209T153000Z DTEND:20210209T163000Z DTSTAMP:20260423T035912Z UID:OAGAS/53 DESCRIPTION:Title: C onvex polytopes that tile space with translations: Voronoi domains and spe ctral sets\nby Alexey Garber (The University of Texas Rio Grande Valle y) as part of Online asymptotic geometric analysis seminar\n\n\nAbstract\n In this talk I am going to discuss convex d-dimensional polytopes that til e R^d with translations and their properties related to two conjectures. T he first conjecture\, the Fuglede conjecture\, claims that every spectral set in R^d tiles the space with translations\; this conjecture was recentl y settled for convex domains by Lev and Matolcsi. The second conjecture\, the Voronoi conjecture\, claims that every convex polytope that tiles R^d with translations is the Voronoi domain for some d-dimensional lattice. Th e conjecture originates from the Voronoi�s geometric theory of positive definite quadratic forms and is related to many questions in mathematical crystallography including Hilbert�s 18th problem. I mostly plan to discu ss recent progress in the Voronoi conjecture and the proof of the conjectu re for five-dimensional parallelohedra\; in the general setting the Vorono i conjecture is still open. The talk is based on a joint work with Alexand er Magazinov (Skoltech).\n LOCATION:https://researchseminars.org/talk/OAGAS/53/ END:VEVENT END:VCALENDAR