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SUMMARY:Gal Dor (TAU)
DTSTART:20200605T133000Z
DTEND:20200605T143000Z
DTSTAMP:20260423T041353Z
UID:AlgWies/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AlgWies/5/">
 Algebraic structures on automorphic L-functions</a>\nby Gal Dor (TAU) as p
 art of Seminar on Representation Theory and Algebraic Geometry\n\n\nAbstra
 ct\nConsiderthe function field $F$ of a smooth curve over $\\mathbb{F}_q$\
 , with $q\\neq 2$.\n\nL-functions of automorphic representations of $\\GL(
 2)$over $F$ are important objects for studying the arithmetic properties o
 f thefield $F$. Unfortunately\, they can be defined in two different ways:
  one byGodement-Jacquet\, and one by Jacquet-Langlands. Classically\, one 
 shows that theresulting L-functions coincide using a complicated computati
 on.\n\n \n\nI will present a conceptual proof that the two familiescoincid
 e\, by categorifying the question. This correspondence will necessitatecom
 paring two very different sets of data\, which will have significantimplic
 ations for the representation theory of $\\GL(2)$. In particular\, we will
 obtain an exotic symmetric monoidal structure on the category ofrepresenta
 tions of $\\GL(2)$\n
LOCATION:https://researchseminars.org/talk/AlgWies/5/
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