BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Huajie Li (Aix-Marseille Université) DTSTART:20210302T153000Z DTEND:20210302T163000Z DTSTAMP:20260423T124739Z UID:MITNT/21 DESCRIPTION:Title: A n infinitesimal variant of Guo-Jacquet trace formulae and its comparison\nby Huajie Li (Aix-Marseille Université) as part of MIT number theory seminar\n\n\nAbstract\nThe Guo-Jacquet conjecture is a promising generaliz ation to higher dimensions of Waldspurger’s well-known theorem relating toric periods to central values of automorphic L-functions for $GL(2)$. Fe igon-Martin-Whitehouse have proved some cases of this conjecture using sim ple relative trace formulae\, Guo’s work on the fundamental lemma and C. Zhang’s work on the transfer. However\, if we want to obtain more gener al results\, we have to establish and compare more general relative trace formulae\, where some analytic difficulties such as the divergence issue s hould be addressed. \n\nIn this talk\, we plan to study analogues of these problems at the infinitesimal level. After briefly introducing the backgr ound\, we shall present an infinitesimal variant of Guo-Jacquet trace form ulae. To compare regular semi-simple terms in these formulae\, we shall di scuss the weighted fundamental lemma and certain identities between Fourie r transforms of local weighted orbital integrals. During the proof\, we al so need some results in local harmonic analysis such as local trace formul ae for some $p$-adic infinitesimal symmetric spaces. This talk is based on my thesis supervised by P.-H. Chaudouard.\n LOCATION:https://researchseminars.org/talk/MITNT/21/ END:VEVENT END:VCALENDAR