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SUMMARY:Ana Caraiani (Imperial College London)
DTSTART:20201103T153000Z
DTEND:20201103T163000Z
DTSTAMP:20260423T125842Z
UID:MITNT/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/13/">V
 anishing theorems for Shimura varieties</a>\nby Ana Caraiani (Imperial Col
 lege London) as part of MIT number theory seminar\n\n\nAbstract\nThe Langl
 ands program is a vast network of conjectures that connect number theory t
 o other areas of mathematics\, such as representation theory and harmonic 
 analysis. The global Langlands correspondence can often be realised throug
 h the cohomology of Shimura varieties\, which are certain moduli spaces eq
 uipped with many symmetries. In this talk\, I will survey some recent vani
 shing results for the cohomology of Shimura varieties with mod $p$ coeffic
 ients and mention several applications to the Langlands program and beyond
 . I will discuss some results that have an $\\ell$-​adic flavour\, where
  $\\ell$ is a prime different from $p$\, that are primarily joint work wit
 h Peter Scholze. I will then mention some results that have a $p$-​adic 
 flavour\, that are primarily joint work with Dan Gulotta and Christian Joh
 ansson. I will highlight the different kinds of techniques that are needed
  in these different settings using the toy model of the modular curve.\n\n
 There are two papers that contain work related to this talk: <a href="http
 s://arxiv.org/abs/1909.01898">arXiv:1909.01898</a> and <a href="https://ar
 xiv.org/abs/1910.09214">arXiv:1910.0914</a>.\n
LOCATION:https://researchseminars.org/talk/MITNT/13/
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