BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Siqi Yang (Imperial) DTSTART:20241120T160000Z DTEND:20241120T170000Z DTSTAMP:20260418T065435Z UID:LNTS/145 DESCRIPTION:Title: H ilbert modular forms and geometric modularity in quadratic case\nby Si qi Yang (Imperial) as part of London number theory seminar\n\nLecture held in Huxley 140\, Imperial College.\n\nAbstract\nLet \\rho: G_\\Q \\rightar row \\GL_2(\\Fpbar) be a continuous\, odd\, irreducible representation. Th e weight part of Serre's conjecture predicts the minimal weight k (\\geq 2 ) such that \\rho arises from a modular eigenform of weight k. It is refin ed by Edixhoven to include the weight one forms by viewing mod p modular f orms as sections of certain line bundles on the special fibre of a modular curve. One of the directions to generalise the weight part of Serre's con jecture is replacing Q with a totally real field F and replacing modular f orms with Hilbert modular forms. A conjecture in this setting is formulate d by Buzzard\, Diamond and Jarvis\, where we have the notion of algebraic modularity. On the other hand\, a generalisation of Edixhoven's refinement is considered by Diamond and Sasaki\, where we have the notion of geometr ic modularity. I will discuss the relation between algebraic and geometric modularity and show their consistency for the weights in a certain cone\, under the assumption that F is a real quadratic field in which p is unram ified.\n LOCATION:https://researchseminars.org/talk/LNTS/145/ END:VEVENT END:VCALENDAR