BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexandre Afgoustidis (CNRS\, l’Institut Élie Cartan de Lorrain e) DTSTART:20210519T150000Z DTEND:20210519T160000Z DTSTAMP:20260420T052726Z UID:NYC-NCG/55 DESCRIPTION:Title: The tempered dual of real or p-adic reductive groups\, and its noncommuta tive geometry (joint work with Anne-Marie Aubert)\nby Alexandre Afgous tidis (CNRS\, l’Institut Élie Cartan de Lorraine) as part of Noncommuta tive geometry in NYC\n\n\nAbstract\nSuppose G is a real or p-adic reductiv e group. The space of irreducible tempered representations of G comes equi pped with the Fell topology\, which encodes important phenomena in represe ntation theory. The topology is usefully studied by noncommutative-geomet ric methods: the tempered dual naturally identifies with the spectrum of t he C*-algebra of G\, and its connected components identify with the spectr a of certain `blocks’ in the C*-algebra. \n\nFor real reductive groups\, A. Wassermann proved in 1987 that each `block’ has\, up to Morita equiv alence\, a beautiful and simple structure. This was a crucial step in his proof of the Baum-Connes-Kasparov conjecture for G. For p-adic groups\, it is not obvious at all that such a structure can exist\, but important exa mples were given by R. Plymen and his students. \n\nIn my talk\, I will re port on joint work with Anne-Marie Aubert which (1) for arbitrary G\, give s a geometric condition for the existence of a Wassermann-type structure o n a given block\, and (2) when G is a quasi-split symplectic\, orthogonal or unitary group\, explicitly determines the connected components of the t empered dual for which the geometric assumption is satisfied.\n LOCATION:https://researchseminars.org/talk/NYC-NCG/55/ END:VEVENT END:VCALENDAR