Relative Langlands duality, past and future
Yiannis Sakellaridis (Johns Hopkins University)
Abstract: Since Riemann's 1859 report on the zeta function, it is known that certain automorphic $L$-functions can be represented as ("period") integrals, which often proves analytic properties such as the functional equation. The method was advanced by Jacquet, Piatetski-Shapiro, Rallis, and many others since the 1970s, giving rise to the "relative" Langlands program. It turns out that the relationship between periods and $L$-functions reflects a duality between certain Hamiltonian varieties for a reductive group and its Langlands dual group. I will set up this duality in a limited setting (joint work with David Ben-Zvi and Akshay Venkatesh), and speculate on how it might be expanded in the future.
number theory
Audience: researchers in the topic
| Organizers: | Sol Friedberg*, Benjamin Howard, Dubi Kelmer, Spencer Leslie, Keerthi Madapusi Pera, Bjorn Poonen*, Andrew Sutherland*, Wei Zhang* |
| *contact for this listing |