Title: Spectral projections on hyperbolic surfaces
Abstract: In an ongoing collaboration with Pierre Germain (Imperial College) and Tristan Léger (NYU and Princeton University), we study $L^2 \to L^p$ estimates (p>2) for spectral projections in a small window on (locally) symmetric spaces. For hyperbolic surfaces of infinite area and with no cusps, we have recently obtained almost optimal results [arXiv:2306.12827]. In this talk, I will give a brief survey of the problem, which goes back to the restriction theorem of Stein-Tomas in the Euclidean setting, comment on our result for hyperbolic surfaces and present the main steps of its proof.
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