BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Toshiyuki Kobayashi (The University of Tokyo) DTSTART:20210908T070000Z DTEND:20210908T075000Z DTSTAMP:20260404T094534Z UID:AIM-RTNCG-SemRepTh/1 DESCRIPTION:Title: Tempered representations and limit algebras\nby Tosh iyuki Kobayashi (The University of Tokyo) as part of Seminar in Representa tion Theory\n\n\nAbstract\nI plan to discuss some new connection between t he following four (apparently un-\nrelated) topics:\n\n(1) (analysis) Temp ered unitary representations on homogeneous spaces\n\n(2) (combinatorics) Convex polyhedral cones\n\n(3) (topology) Limit algebras\n\n(4) (symplecti c geometry) Quantization of coadjoint orbits\,\n\nbased on a series of joi nt papers with Y. Benoist "Tempered homogeneous spaces\nI–IV".\n LOCATION:https://stable.researchseminars.org/talk/AIM-RTNCG-SemRepTh/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Chen-Bo Zhu (National University of Singapore) DTSTART:20210908T075000Z DTEND:20210908T084000Z DTSTAMP:20260404T094534Z UID:AIM-RTNCG-SemRepTh/2 DESCRIPTION:Title: Theta correspondence and special unipotent representatio ns\nby Chen-Bo Zhu (National University of Singapore) as part of Semin ar in Representation Theory\n\n\nAbstract\nThe theory of theta corresponde nce\, initiated by Howe\, provides a powerful method of constructing irred ucible admissible representations of classical Lie groups. In this talk\, I will discuss a recent work\, joint with Barbasch\, Ma and Sun\, in which we show that in addition to irreducible unitary parabolic inductions\, th eta lifts yield all special unipotent representations of a classical Lie g roup $G$. As a consequence of the construction and the classification\, we conclude that all special unipotent representations of $G$ are unitarizab le\, as predicted by the Arthur--Barbasch--Vogan conjecture.\n LOCATION:https://stable.researchseminars.org/talk/AIM-RTNCG-SemRepTh/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Wee Teck Gan (National University of Singapore) DTSTART:20210908T090000Z DTEND:20210908T095000Z DTSTAMP:20260404T094534Z UID:AIM-RTNCG-SemRepTh/3 DESCRIPTION:Title: Twisted GGP problems and conjectures\nby Wee Teck Ga n (National University of Singapore) as part of Seminar in Representation Theory\n\n\nAbstract\nI will discuss some twisted variants of the GGP rest riction problems in the setting of skew-Hermitian spaces. Together with Gr oss and Prasad\, we formulate conjectural answers to these twisted GGP pro blems and provide some evidences in low rank and for unitary principal ser ies.\n LOCATION:https://stable.researchseminars.org/talk/AIM-RTNCG-SemRepTh/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Binyong Sun (Zhejiang University) DTSTART:20210909T070000Z DTEND:20210909T075000Z DTSTAMP:20260404T094534Z UID:AIM-RTNCG-SemRepTh/4 DESCRIPTION:Title: Archimedean period relations and period relations for au tomorphic L-functions\nby Binyong Sun (Zhejiang University) as part of Seminar in Representation Theory\n\n\nAbstract\nIt was known to Euler tha t $\\zeta(2k)$ is a rational multiple of $\\pi^{2k}$\, where $\\zeta$ is t he Euler--Riemann zeta function\, and $k$ is a positive integer. Following the pioneering works of G. Shimura\, P. Deligne and etc.\, D. Blasius pro posed a conjecture which asserts that similar rationality results hold for very general automorphic L-functions. We confirm Blasius's conjecture in two cases: the standard L-functions of symplectic type (joint with Dihua J iang and Fangyang Tian)\, and the Rankin-Selberg L-functions for $\\operat orname{GL}(n)\\times\\operatorname{GL}(n-1)$ (joint with Jian-Shu Li and D ongwen Liu). The key ingredient is the Archimedean period relations for th e modular symbols at infinity. These two cases have already been studied b y many authors\, including Harris--Lin\, Grobner--Raghuram\, Harder--Raghu ram\, Januszewski\, Grobner--Lin\, and etc.\n LOCATION:https://stable.researchseminars.org/talk/AIM-RTNCG-SemRepTh/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Yoshiki Oshima (Osaka University) DTSTART:20210909T081000Z DTEND:20210909T090000Z DTSTAMP:20260404T094534Z UID:AIM-RTNCG-SemRepTh/5 DESCRIPTION:Title: On the asymptotic support of Plancherel measures for hom ogeneous spaces\nby Yoshiki Oshima (Osaka University) as part of Semin ar in Representation Theory\n\n\nAbstract\nLet $G$ be a real reductive gro up and $X$ a homogeneous $G$-manifold. The Plancherel measure for $X$ desc ribes how $L^2(X)$ breaks up into irreducible unitary representations of $ G$. We discuss asymptotics of the support of Plancherel measure and relate it with geometry of coadjoint orbits. In particular\, we give a sufficien t condition for the existence of discrete series. This is a joint work wit h Benjamin Harris.\n LOCATION:https://stable.researchseminars.org/talk/AIM-RTNCG-SemRepTh/5/ END:VEVENT END:VCALENDAR