BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tony Feng (MIT/IAS) DTSTART:20201210T170000Z DTEND:20201210T182000Z DTSTAMP:20260423T021257Z UID:RAMpAGe/26 DESCRIPTION:Title: Equivariant localization\, parity sheaves\, and cyclic base change\nb y Tony Feng (MIT/IAS) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nLafforgue and Genestier-Lafforgue have constru cted the global and (semisimplified) local Langlands correspondences for arbitrary reductive groups over function fields. I will explain some rece ntly established properties of these correspondences regarding base change functoriality: existence of transfers for mod $p$ automorphic forms throu gh $p$-cyclic base change in the global correspondence\, and Tate cohomolo gy realizes $p$-cyclic base change in the mod $p$ local correspondence. In particular\, the local statement verifies a conjecture\nof Treumann-Venka tesh. The proofs combine Lafforgue’s theory with equivariant localizatio n arguments for shtukas as well as recent advances in modular representati on theory\, namely parity sheaves and Smith-Treumann theory. Compared with previous iterations of the talk\,\nthis time the talk will emphasize the role of the new representation-theoretic tools\, during the extra 20 minut es.\n LOCATION:https://researchseminars.org/talk/RAMpAGe/26/ END:VEVENT END:VCALENDAR