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Automorphic forms, L-functions, and the conformal bootstrap

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OOEW12 - Physics and automorphic L-functions: gravity, conformal field theory and number theory

I will review an analogy between conformal field theory in d dimensions, and spectral theory of automorphic forms on hyperbolic (d+1)-manifolds. Building on this analogy, I will prove a new subconvex bound on triple product L-functions, using the conformal bootstrap. Finally, I will review a theorem of Adve that the bootstrap method knows all there is to know about the spectra and trilinear periods of compact hyperbolic surfaces. Based on works with A. Adve, J. Bonifacio, P. Kravchuk, S. Pal, A. Radcliffe, and G. Rogelberg.

This talk is part of the Isaac Newton Institute Seminar Series series.

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Elton Bowring Room, Gillespie Centre, Clare College Lecture Theatre 2, Computer Laboratory, William Gates Building Marine/Wolfson Building lecture hall - Bullard Labs

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