Title: Summation formulae and triple product L-functions

Abstrct:In 2000 Braverman and Kazhdan introduced an ambitious program to study Langlands L-functions using conjectural generalizations of the Poisson summation formula.  As emphasized by Sakellaridis, the most natural setting for their conjectures is the theory of spherical varieties.  We will explore two closely related families of spherical varieties.  For one we have a robust Poisson summation formula due to the speaker and his coauthors Hsu, Liu, and Leslie.  The other gives an integral representation for triple product L functions in arbitrary rank.  Time permitting, we will discuss the possibility of bridging the gap between these two families.