# The Plancherel formula for L^2(GL_n(F)\GL_n(E)) and applications to the Ichino-Ikeda and formal degree conjectures for unitary groups

 Workshop on Representation Theory and Analysis on Locally Symmetric Spaces Topic: The Plancherel formula for L^2(GL_n(F)\GL_n(E)) and applications to the Ichino-Ikeda and formal degree conjectures for unitary groups Speaker: Raphael Beuzart-Plessis Affiliation: CNRS Date: Tuesday, March 6 Time/Room: 11:30am - 12:30pm/Simonyi Hall 101

Abstract : Let $E/F$ be a quadratic extension of local fields of characteristic zero. In this talk, I will explain two ways to compute the Plancherel decomposition of $L^2(GL_n(F)\backslash GL_n(E))$. In both cases, the result involves the image of base change from unitary groups to $GL_n(E)$ and is in accordance with a general conjecture of Sakellaridis-Venkatesh on the spectral decomposition of spherical varieties. We will also give applications of our formulas to the so-called Ichino-Ikeda and formal degree conjectures for unitary groups.