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A relative trace formula comparison for the global Gross-Prasad conjecture for orthogonal groups

Algebra and Number Theory Seminar

A relative trace formula comparison for the global Gross-Prasad conjecture for orthogonal groups
Series: Algebra and Number Theory Seminar
Location: ENR2 S395
Presenter: Rahul Krishna, Brandeis University

The global Gross-Prasad conjecture (really its refinement by Ichino and Ikeda) is a remarkable conjectural formula generalizing Waldspurger's formula for the central value of a Rankin-Selberg $L$ function. I will explain a relative trace formula approach to this conjecture, akin in spirit to the successful comparison for unitary groups. The approach relies on a somewhat strange matching of orbits, and on two local conjectures of smooth transfer and fundamental lemma type, which I will formulate. I will discuss some recent evidence for these local identities in some low rank cases.