BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jessica Fintzen (IAS\, Cambridge University\, Duke University) DTSTART:20201215T140000Z DTEND:20201215T150000Z DTSTAMP:20260418T094813Z UID:NTRV/2 DESCRIPTION:Title: Rep resentations of $p$-adic groups and applications\nby Jessica Fintzen ( IAS\, Cambridge University\, Duke University) as part of Number Theory and Representations in Valparaiso\n\n\nAbstract\nThe Langlands program is a f ar-reaching collection of conjectures that relate different areas of mathe matics including number theory and representation theory. A fundamental pr oblem on the representation theory side of the Langlands program is the co nstruction of all (irreducible\, smooth\, complex) representations of $p$- adic groups. I will provide an overview of our understanding of the repres entations of $p$-adic groups\, with an emphasis on recent progress.\n\nI w ill also outline how new results about the representation theory of $p$-ad ic groups can be used to obtain congruences between arbitrary automorphic forms and automorphic forms which are supercuspidal at $p$\, which is join t work with Sug Woo Shin. This simplifies earlier constructions of attachi ng Galois representations to automorphic representations\, i.e. the global Langlands correspondence\, for general linear groups. Moreover\, our resu lts apply to general $p$-adic groups and have therefore the potential to b ecome widely applicable beyond the case of the general linear group.\n LOCATION:https://researchseminars.org/talk/NTRV/2/ END:VEVENT END:VCALENDAR