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.
.