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.