BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Linus Hamann (Harvard University) DTSTART:20241125T210000Z DTEND:20241125T220000Z DTSTAMP:20260423T040624Z UID:NTBU/11 DESCRIPTION:Title: Sh imura Varieties and Eigensheaves\nby Linus Hamann (Harvard University) as part of Boston University Number Theory Seminar\n\nLecture held in CDS Room 365 in Boston University.\n\nAbstract\nThe cohomology of Shimura var ieties is a fundamental object of study in algebraic number theory by virt ue of the fact that it is the only known geometric realization of the glob al Langlands correspondence over number fields. Usually\, the cohomology i s computed through very delicate techniques involving the trace formula. H owever\, this perspective has several limitations\, especially with regard s to questions concerning torsion. In this talk\, we will discuss a new p aradigm for computing the cohomology of Shimura varieties by decomposing c ertain sheaves coming from Igusa varieties into Hecke eigensheaves on the moduli stack of G-bundles on the Fargues-Fontaine curve. Using this point of view\, we will describe several conjectures on the torsion cohomology o f Shimura varieties after localizing at suitably “generic” L-parameter s\, as well as some known results in the case that the parameter factors t hrough a maximal torus. Motivated by this\, we will sketch part of an emer ging picture for describing the cohomology beyond this generic locus by co nsidering certain “generalized eigensheaves” whose eigenvalues are spr ead out in multiple cohomological degrees based on the size of a certain A rthur SL_{2} in a way that is reminiscent of Arthur’s cohomological conj ectures on the intersection cohomology of Shimura Varieties. This is based on joint work with Lee\, joint work in progress with Caraiani and Zhang\, and conversations with Bertoloni-Meli and Koshikawa.\n LOCATION:https://researchseminars.org/talk/NTBU/11/ END:VEVENT END:VCALENDAR