BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Shenghao Li (Maryland) DTSTART:20260114T230000Z DTEND:20260115T000000Z DTSTAMP:20260423T040042Z UID:UtahRTNT/10 DESCRIPTION:Title: Base change fundamental lemma for Bernstein centers of principal series blocks\nby Shenghao Li (Maryland) as part of University of Utah Repres entation Theory / Number Theory Seminar\n\nLecture held in LCB 222.\n\nAbs tract\nLet G be an unramified group over a p-adic field F\, and F_r/F an u nramified extension of degree r. Let H(G) (resp. H(G(F_r)) denote the Heck e algebra of G(F) (resp. G(F_r)). Roughly speaking\, we say two functions \\phi\\in H(G(F_r)) and f\\in H(G) are associated (or matching functions) if they have the same stable orbital integrals. One main question is: how can we construct matching functions? In 1986\, Kottwitz proved the unit el ements of some Hecke algebras are associated. In 1990\, Clozel defined a b ase change map between spherical Hecke algebras and proved the two functio ns corresponded by the base change map are associated. Later in 2009 and 2 012\, Haines generalized Clozel's result to centers of parahoric Hecke alg ebras and Bernstein centers of depth zero principal series block. In this talk\, we will briefly introduce the history and set up of base change fun damental lemma\, and focus on how we can generalize the result to general principal series blocks. This requires the concrete constructions of types for principal series blocks of unramified groups\, and some concrete comp utations of root groups\, which might give some inspirations on future stu dy on deeper level structures.\n LOCATION:https://researchseminars.org/talk/UtahRTNT/10/ END:VEVENT END:VCALENDAR