BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ivo Dell'Ambrogio (Université de Lille\, France) DTSTART:20201130T150000Z DTEND:20201130T160000Z DTSTAMP:20260404T163346Z UID:QGS/4 DESCRIPTION:Title: The spectrum of equivariant Kasparov theory for cyclic groups of prime order\nby Ivo Dell'Ambrogio (Université de Lille\, France) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nIn 2006\, Ralf Meyer and Rysz ard Nest proved that the G-equivariant Kasparov category of a locally comp act group G carries the structure of a tensor-triangulated category. This structure conveniently handles the usual homological algebra\, bootstrap c onstructions and assembly maps involved in many KK-theoretical calculation s\, e.g. in connection with the Baum-Connes conjecture. As with any tenso r triangulated category\, we can also associate to the G-equivariant Kaspa rov category its spectrum in the sense of Paul Balmer. This is a topologic al space (similar to the Zariski spectrum of a commutative ring) which all ows us\, as it were\, to re-inject some genuinely geometric ideas in non-c ommutative geometry. It turns out that the spectrum contains enough inform ation to prove the Baum-Connes conjecture for G\, hence we should expect t he question of its computation to be very hard. In this talk\, after disc ussing such preliminaries and motivation\, I will present joint work with Ralf Meyer providing the state of the art on this subject. Although more g eneral partial results are known\, a complete answer is only known so far for finite groups of prime order and for algebras in the bootstrap categor y.\n LOCATION:https://stable.researchseminars.org/talk/QGS/4/ END:VEVENT END:VCALENDAR