BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Matthias Strauch (Indiana University) DTSTART:20261104T160000Z DTEND:20261104T170000Z DTSTAMP:20261111T134035Z UID:FGC-IPM/70 DESCRIPTION:Title: Block decompositions in the local p-adic Langlands program\nby Matthi as Strauch (Indiana University) as part of FGC-HRI-IPM Number Theory Webin ars\n\n\nAbstract\nLet F be a finite extension of the field of p-adic numb ers.\nThe classical local Langlands correspondence relates complex\nrepres entations of the Galois group of F (more precisely of the\nWeil-Deligne gr oup of F) to so-called smooth representations of the\ngroup G = GL_n(F) on complex vector spaces. Using the concept of a\ncenter of a category\, Jos eph Bernstein has described the decomposition\ninto blocks of the category of those smooth representations of G. The\nblocks are parametrized by "cu spidal data"\, which in turn consist of\n(equivalence classes of) Levi sub groups and supercuspidal\nrepresentations of the latter. The category is t hus highly disconnected\,\nas there is no way to "interpolate" between dif ferent Levi subgroups and\ndifferent supercuspidal representations. In thi s talk we will consider\nso-called locally analytic representations of G o n p-adic vector spaces\nand see that the category of those representations decomposes into only\nfinitely many blocks.\n\n We will put this result into the context of a localization theory for\nthose representations propo sed by Emerton-Gee-Hellmann\, and see that\nthis block decomposition has a geometric analogue in terms of the\nEmerton-Gee stack of (phi\,Gamma)-mod ules. This is joint work with Daniel\nLe and Zichuan Wang.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/70/ END:VEVENT END:VCALENDAR