BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tsachik Gelander (Weizmann Institute of Science) DTSTART:20200520T111000Z DTEND:20200520T123000Z DTSTAMP:20260423T004729Z UID:GDS/4 DESCRIPTION:Title: Conv ergence of normalized Betti numbers in nonpositive curvature\nby Tsach ik Gelander (Weizmann Institute of Science) as part of Geometry and Dynami cs seminar\n\n\nAbstract\nI will show that if X is any symmetric space oth er than 3-dimensional \nhyperbolic space and M is any finite volume manifo ld that is a quotient \nof X\, then the normalized Betti numbers of M are "testable"\, i.e. one \ncan guess their values by sampling the manifold at random places. This \nis joint with Abert\, Biringer and Bergeron\, and e xtends some of our \nolder work with Nikolov\, Raimbault and Samet. The co ntent of the recent \npaper involves a random discretization process that converts the "thick \npart" of M into a simplicial complex\, together with analysis of the \n"thin parts" of M. As a corollary\, we obtain that when ever X is a higher \nrank irreducible symmetric space and M_i is any seque nce of distinct \nfinite volume quotients of X\, the normalized Betti numb ers of the M_i \nconverge to the "L^2-Betti numbers" of X.\n LOCATION:https://researchseminars.org/talk/GDS/4/ END:VEVENT END:VCALENDAR