## Arithmetic Geometry and Number Theory RTG Seminar: Towards the global Gross-Prasad conjecture for orthogonal groups

Seminar | February 26 | 3:10-5 p.m. | 748 Evans Hall

Rahul Krishna, Northwestern University

Department of Mathematics

Seminar Format: The seminar consists of two 50-minute talks, a pre-talk (3:10-4:00) and an advanced talk (4:10-5:00), with a 10-minute break (4:00-4:10) between them. The advanced talk is a regular formal presentation about recent research results to general audiences in arithmetic geometry and number theory; the pre-talk (3:10-4:00) is to introduce some prerequisites or background for the advanced talk to audiences consisting of graduate students.

Abstract of pre-talk: I will explain some background material on the relative trace formula and its uses. As illustration, I will recall the statement of Waldspurger's formula for toric periods on $PGL_2$ and sketch Jacquet's trace formula proof of this beautiful result.

Abstract of main talk: The global Gross-Prasad conjecture and its refinement by Ichino and Ikeda posit a tight relationship between the central value of an automorphic $L$-function and a certain automorphic period integral on orthogonal groups. In this talk, I will explain the construction of two relative trace formulas that encode the $L$-value and period integral that appear in this conjecture; I will also outline a potential comparison between these trace formulas, and provide some evidence for the usefulness of this comparison in low rank. This is work in progress, and may be subject to change.

yxy@berkeley.edu