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Eigenfunction and spectral projection estimates on hyperbolic surfaces

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GSTW01 - High energy spectral theory: geometry and dynamics

We will discuss L2 to Lq bounds for spectral projection operators on logarithmic intervals on hyperbolic manifolds. In dimension two, we will describe an application of these bounds to the Lq’ to Lq mapping properties of the spectral measure on convex cocompact hyperbolic surfaces. If time permits, we will also discuss recent ongoing work on improved L^q estimates for arithmetic eigenfunctions. This is based on joint work with Jiaqi Hou, Chris Sogge, Zhexing Zhang and Zhongkai Tao.

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

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