BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Miriam Norris (Queen Mary University of London) DTSTART:20251209T140000Z DTEND:20251209T150000Z DTSTAMP:20260421T154340Z UID:UEAPS/66 DESCRIPTION:Title: O n $p$-ordinary mod $p$ local Langlands correspondences.\nby Miriam Nor ris (Queen Mary University of London) as part of ANTLR seminar\n\nLecture held in NEWSCI 0.04.\n\nAbstract\nTo a suitably “nice” automorphic rep resentation\, we can attach a $p$-adic representation of the absolute Galo is group of a number field. We call a Galois representation arising in thi s way automorphic. One of the goals of the Langlands programme is to class ify the image of automorphic Galois representations within the set of all Galois representations\, thereby establishing a correspondence.\n\nWhen $n =2$ and the number field is $\\mathbb{Q}$\, such a correspondence has been constructed by combining mod $p$ and $p$-adic correspondences with local –global compatibility results. In particular\, the $p$-adic corresponden ce is a representation of $GL_2(\\mathbb{Q}_p)$\, associated to a local Ga lois representation\, which appears in the cohomology of the modular curve .\n\nIn work of Breuil and Herzig\, a candidate for a more general corresp ondence for $p$-ordinary local Galois representations was constructed. In this talk I will discuss joint work with Shu Sasaki in which we construct a framework that should generalise Breuil and Herzig's construction\, in p articular allowing for the non-generic case.\n LOCATION:https://researchseminars.org/talk/UEAPS/66/ END:VEVENT END:VCALENDAR