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Jonathan Wang, RLM 9.166: Geometric asymptotics for spherical varieties
Thursday, February 13, 2020, 03:30pm - 04:30pm
There are many examples in number theory where an L-function has an integral representation related to a subgroup of G, with the first example going back to Hecke. Sakellaridis and Venkatesh have formulated a unified framework to study this connection through the lens of spherical varieties. In particular, in the local setting there is expected to be a relation between certain local L-factors and the asymptotic expansion of a "basic function" on a spherical variety over a p-adic local field. Over a function field, this basic function is expected to correspond, under the functions-sheaves dictionary, to the IC complex of an (infinite dimensional) formal arc space. In this talk, we discuss work in progress with Sakellaridis on how to "categorify" and compute the desired asymptotics using nearby cycles. ​
Location: RLM 9.166

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