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SUMMARY:Jessica Fintzen (Cambridge/Duke/IAS)
DTSTART:20200908T143000Z
DTEND:20200908T153000Z
DTSTAMP:20260423T125419Z
UID:MITNT/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/6/">Re
 presentations of p-adic groups and applications</a>\nby Jessica Fintzen (C
 ambridge/Duke/IAS) as part of MIT number theory seminar\n\n\nAbstract\nThe
  Langlands program is a far-reaching collection of conjectures that relate
  different areas of mathematics including number theory and representation
  theory. A fundamental problem on the representation theory side of the La
 nglands program is the construction of all (irreducible\, smooth\, complex
 ) representations of p-adic groups. \n\nI will provide an overview of our 
 understanding of the representations of p-adic groups\, with an emphasis o
 n recent progress. \n\nI will also outline how new results about the repre
 sentation theory of p-adic groups can be used to obtain congruences betwee
 n arbitrary automorphic forms and automorphic forms which are supercuspida
 l at p\, which is joint work with Sug Woo Shin. This simplifies earlier co
 nstructions of attaching Galois representations to automorphic representat
 ions\, i.e. the global Langlands correspondence\, for general linear group
 s. Moreover\, our results apply to general p-adic groups and have therefor
 e the potential to become widely applicable beyond the case of the general
  linear group.\n\nNote the this talk will take place at 10:30 rather than 
 16:30 (Eastern time).\n
LOCATION:https://researchseminars.org/talk/MITNT/6/
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