BEGIN:VCALENDAR VERSION:2.0 PRODID:-//jEvents 2.0 for Joomla//EN CALSCALE:GREGORIAN METHOD:PUBLISH BEGIN:VTIMEZONE TZID:America/New_York BEGIN:STANDARD DTSTART:20201101T010000 RDATE:20210314T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20211107T010000 RDATE:20220313T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20221106T010000 RDATE:20230312T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20231105T010000 RDATE:20240310T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20241103T010000 RDATE:20250309T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20251102T010000 RDATE:20260308T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20261101T010000 RDATE:20270314T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20271107T010000 RDATE:20280312T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20281105T010000 RDATE:20290311T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:DAYLIGHT DTSTART:20200420T153000 RDATE:20201101T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20210314T030000 RDATE:20211107T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20220313T030000 RDATE:20221106T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20230312T030000 RDATE:20231105T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20240310T030000 RDATE:20241103T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20250309T030000 RDATE:20251102T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20260308T030000 RDATE:20261101T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20270314T030000 RDATE:20271107T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20280312T030000 RDATE:20281105T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT END:VTIMEZONE BEGIN:VEVENT UID:16c52a918e07166496555a39b0545eb4 CATEGORIES:Colloquia CREATED:20210420T082205 SUMMARY:Vinberg’s theory of hyperbolic reflection groups LOCATION:Zoom DESCRIPTION:Abstract: This talk is devoted to the memory of my teacher, Professor Ernes t Borisovich Vinberg: 1937 -- 2020. All of us are familiar with the kaleido scope, in which multicolored glasses form an attractive and amazing reflect ion pattern. Such pictures are obtained by a system of reflections with res pect to certain mirrors. Generalizing this concept, we may consider discret e reflection groups of finite covolume in Euclidean spaces E^n and on the s pheres S^n. Such were studied by many mathematicians and finally classified completely by Coxeter in 1933 via Coxeter diagrams. They exist in all dime nsions n for both E^n and S^n.\nThe story of reflection groups in hyperboli c Lobachevsky spaces H^n (and to the phenomenal impact of Vinberg in this t heory) goes back to the 19th century, to the works of Poincare and Dyck abo ut the classification of Fuchsian groups. However only low-dimensional exam ples of such groups were known. In 1967, Vinberg initiated his fundamental theory of hyperbolic reflection groups. In 1972, he suggested an algorithm for constructing the fundamental Coxeter polytope of an arbitrary hyperboli c reflection group. The Vinberg algorithm is now widely used by many people in different branches of mathematics. In 1981, Vinberg obtained the follow ing celebrated and surprising result: there are no compact hyperbolic Coxet er polytopes and no arithmetic finite volume Coxeter polytopes in H^n with n>29. With these results, Vinberg was selected as an Invited Speaker at the ICM 1983. In 2014, he constructed the first examples of higher-dimensio nal non-arithmetic non-compact hyperbolic Coxeter polytopes.\n X-ALT-DESC;FMTTYPE=text/html:

Abstract: This talk is devoted to the memory of my teacher, Professor Ernest Borisovich Vinberg: 1 937 -- 2020. All of us are familiar with the kaleidoscope, in which multico lored glasses form an attractive and amazing reflection pattern. Such pictu res are obtained by a system of reflections with respect to certain mirrors . Generalizing this concept, we may consider discrete reflection groups of finite covolume in Euclidean spaces E^n and on the spheres S^n. Such were s tudied by many mathematicians and finally classified completely by Cox eter in 1933 via Coxeter diagrams. They exist in all dimensions n for both E^n and S^n.

The story of reflection groups in hyperbolic Lobach evsky spaces H^n (and to the phenomenal impact of Vinberg in this theory) g oes back to the 19th century, to the works of Poincare and Dyck about the c lassification of Fuchsian groups. However only low-dimensional examples of such groups were known. In 1967, Vinberg initiated his fundamental theory o f hyperbolic reflection groups. In 1972, he suggested an algorithm for cons tructing the fundamental Coxeter polytope of an arbitrary hyperbolic reflec tion group. The Vinberg algorithm is now widely used by many people in diff erent branches of mathematics. In 1981, Vinberg obtained the following cele brated and surprising result: there are no compact hyperbolic Coxeter polyt opes and no arithmetic finite volume Coxeter polytopes in H^n with n>29. With these results, Vinberg was selected as an Invited Speaker at the ICM 1983. In 2014, he constructed the first examples of higher-dimensional non- arithmetic non-compact hyperbolic Coxeter polytopes.

CONTACT:Nikolay Bogachev (Skoltech & MIPT) DTSTAMP:20260828T110907 DTSTART;TZID=America/New_York:20210421T153000 DTEND;TZID=America/New_York:20210421T163000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR