# Transfer operators between relative trace formulas in rank one

Date(s) : 05/06/2018   iCal
14 h 00 min - 15 h 00 min

I will introduce a new paradigm for comparing relative trace formulas, in order to prove instances of (relative) functoriality and relations between periods of automorphic forms and L-functions.
More precisely, for a spherical variety $X=H\backslash G$ of rank one, I will prove that there is an explicit “transfer operator” which transforms the orbital integrals of the relative trace formula for $X \times X/G$ to the orbital integrals of the Kuznetsov formula for $GL(2)$ or $SL(2)$, equipped with suitable non-standard test functions. The operator is determined by the L-value associated to the square of the H-period integral, and the proof uses a deep theory of Friedrich Knop on the cotangent bundles of spherical varieties, viewed as Hamiltonian manifolds.

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