Brandeis Harvard MIT Northeastern Mathematics Colloquium

Thursday, October 04, 2018 at 4:30pm to 5:30pm


Semyon Dyatlov (MIT)

Title: “Fractal uncertainty principle and quantum chaos”

Abstract: Fractal uncertainty principle states that no function can be localized to a fractal set simultaneously in position and in frequency. The strongest version so far has been obtained in one dimension by Bourgain and the speaker with recent higher dimensional advances by Han and Schlag. I will present two applications of the fractal uncertainty principle. The first one (joint with Jin) is a frequency-independent lower bound on mass of eigenfunctions on compact hyperbolic surfaces, which in particular implies control for the Schrödinger equation by any nonempty open set. In work in progress with Jin and Nonnenmacher we handle surfaces of variable negative curvature which present serious new challenges. The second application (joint with Zahl) is an essential spectral gap for convex co-compact hyperbolic surfaces, which implies exponential energy decay of high frequency waves.

Reception: 4:00pm in room 2-290.

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