## Columbia Mathematics Department Colloquium

*L-functions and trace formulas: *

*small steps beyond endoscopy*

by

# Yiannis Sakellaridis

## Rutgers-Newark

Abstract:

The world of
automorphic forms is full of mysteries, such as: L-functions popping up
out of the blue (keywords: periods, Tate integrals, Rankin-Selberg
method); and seemingly unrelated homogeneous spaces having similar
spectra (keywords: functoriality, endoscopy, distinction, spherical
varieties). Most of the talk will be devoted to describing some of
these phenomena to the non-expert audience. Then, I will outline an
attempt to understand some of them through a new approach to the
relative trace formula, which yields a new proof of a celebrated result
of Waldspurger linking toric periods and special values of L-functions.

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