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Mathematics Department Colloquium

  • Date
    Thu, Nov 07

    Time
    1:00 PM — 2:00 PM

    Website
    http://math.sci.ccny.cuny.edu/seminar/show/7

    Address
    NAC
    160 Convent Avenue

    Location
    NAC, 6/113

    p: 212.650.5346

    Admission
    Free

  • Event Details

    Ali Altug (Columbia University), Beyond Endoscopy via the Trace Formula 

    In his recent paper,“Beyond Endoscopy”, Langlands proposed an approach to (ultimately) attack the general functoriality conjectures by means of the trace formula. For a (reductive algebraic) group G over a global field F and a representation ρ : ^{L}G → GL(V), the strategy, among other things, aims at detecting those automorphic representations of G for which the L-function, L(s,π,ρ), has a pole at s = 1. The method suggested using the trace formula together with an averaging process to capture these poles.

    In this talk we will start by recalling the functoriality conjectures and briefly describe the method suggested by Langlands. Then, specializing on the group GL(2) we will discuss some recent work on Beyond Endoscopy. More precisely, we will discuss the elliptic part of the trace formula and the analytic problems caused by the volumes of tori, singularities of orbital integrals and the non-tempered terms. We will then describe how one can use an approximate functional equation in the trace formula to rewrite the elliptic part which resolves these issues. Finally, we will talk about applications of the resulting formula.
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