Resonances on hyperbolic surfaces… and Berkovich space

The HADES seminar on Tuesday, February 20th, will be at 3:30pm in Room 939.

Speaker: Zhongkai Tao

Abstract: Hyperbolic surfaces are surfaces with constant negative curvature -1. They appear in many places: number theory, PDE, geometry, and topology… and they have many special properties. Despite a lot of studies and efforts put into this subject, the spectral theory of hyperbolic surfaces remains mysterious, especially in the infinite volume case. I will introduce some basic notions of the spectral theory on hyperbolic surfaces, and advertise some open problems. Then I will talk about recent developments on degeneration of hyperbolic surfaces, which uses some new tools from non-Archimedean geometry, and how this would potentially help us understand hyperbolic surfaces.

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