# Endoscopy for symmetric varieties

SEMINARS, NUMBER THEORY

##### Speaker:

Spencer Leslie *- Boston College*

Relative trace formulas are central tools in the study of relative functoriality. In many cases of interest, basic stability problems have not previously been addressed. In this talk, I discuss a theory of endoscopy in the context of symmetric varieties with the global goal of stabilizing the associated relative trace formula. I outline how, using the dual group of the symmetric variety, one can give a good notion of endoscopic symmetric variety and conjecture a matching of relative orbital integrals in order to stabilize the relative trace formula, which can be proved in some cases. Time permitting, I will explain my proof of these conjectures in the case of unitary Friedberg–Jacquet periods.