BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Uri Bader (Weizmann Institute of Science) DTSTART:20200624T111000Z DTEND:20200624T123000Z DTSTAMP:20260423T022744Z UID:GDS/10 DESCRIPTION:Title: Tot ally geodesic subspaces and arithemeticity phenomena in hyperbolic manifol ds\nby Uri Bader (Weizmann Institute of Science) as part of Geometry a nd Dynamics seminar\n\n\nAbstract\nIn this talk I will survey a well known \, still wonderful\, connection \nbetween geometry and arithmetics and dis cuss old and new results in \nthis topic. The starting point of the story is Cartan's discovery \nof the correspondence between semisimple Lie group s and symmetric \nspaces. Borel and Harish-Chandra\, following Siegel\, la ter realized \na fantastic further relation between arithmetic subgroups o f semisimple \nLie groups and locally symmetric space - every arithemtic g roup gives \na locally symmetric space of finite volume. The best known ex ample \nis the modular curve which is associated in this way with the grou p \nSL_2(Z). This relation has a partial converse\, going under the name \ n"arithmeticity theorem"\, which was proven\, under a higher rank \nassump tion\, by Margulis and in some rank one situations by Corlette \nand Gromo v-Schoen. The rank one setting is related to hyperbolic \ngeometry - real\ , complex\, quaternionic or octanionic.\nThere are several open questions regarding arithmeticity of locally \nhyperbolic manifolds of finite volume over the real or complex fields \nand there are empirical evidences relat ing these questions to the \ngeometry of totally geodesic submanifolds. \n Recently\, some of these questions were solved by Margulis-Mohammadi \n(re al hyp. 3-dim)\, Baldi-Ullmo (complex hyp.) and B-Fisher-Miller-Stover. \n The techniques involve a mixture of ergodic theory\, algebraic groups \nth eory and hodge theory. After surveying the above story\, explaining \nall the terms and discussing some open questions\, I hope to have a \nlittle t ime to say something about the proofs.\n LOCATION:https://researchseminars.org/talk/GDS/10/ END:VEVENT END:VCALENDAR