BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ryo Toyota (Texas A&M) DTSTART:20251008T190000Z DTEND:20251008T200000Z DTSTAMP:20260420T052915Z UID:NYC-NCG/207 DESCRIPTION:Title: Twisted coarse Baum-Connes conjecture and relatively hyperbolic groups.< /a>\nby Ryo Toyota (Texas A&M) as part of Noncommutative geometry in NYC\n \n\nAbstract\nCoarse Baum-Connes conjecture claims an algorithm to compute the higher index and which has applications to important problems in geom etry\, topology and operator algebras. To verify this conjecture for a lar ger class of metric spaces\, we introduce twisted coarse Baum–Connes con jecture with stable coarse algebras\, which can be viewed as a geometric a nalogue of the Baum–Connes conjecture with coefficients. We show that th is twisted version has stronger permanence properties than the classical c oarse Baum–Connes conjecture\, particularly with respect to unions and s ubspaces. Then\, we apply this framework to relatively hyperbolic groups. For a finitely generated group $G$ that is hyperbolic relative to $\\{H_1 \,\\cdots\,H_n\\}$\, it is known that $G$ satisfies coarse Baum-Connes con jecture if each $H_i$ does and $H_i$ admits finite-dimensional simplicial model of the universal space for proper actions. As a consequence of the p ermanence properties\, we can remove the topological condition of $H_i$ in the aforementioned theorem. Namely\, we show that $G$ satisfies twisted c oarse Baum-Connes conjecture with stable coefficients\, if and only if eac h $H_i$ does. This is a joint work with Jintao Deng.\n LOCATION:https://researchseminars.org/talk/NYC-NCG/207/ END:VEVENT END:VCALENDAR