89 citations · 1.1k across the 43 of their papers we have counts for
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Control of eigenfunctions on hyperbolic surfaces: an application of fractal uncertainty principle
Semyon Dyatlov
This expository article, written for the proceedings of the Journées EDP (Roscoff, June 2017), presents recent work joint with Jean Bourgain [arXiv:1612.09040] and Long Jin [arXiv:…
Fractal uncertainty for transfer operators
Semyon Dyatlov, Maciej Zworski
We show directly that the fractal uncertainty principle of Bourgain-Dyatlov [arXiv:1612.09040] implies that there exists for which the Selberg zeta function for a convex c…
Fourier dimension and spectral gaps for hyperbolic surfaces
Jean Bourgain, Semyon Dyatlov
We obtain an essential spectral gap for a convex co-compact hyperbolic surface which depends only on the dimension of the limit set. More precisely,…
Semiclassical measures on hyperbolic surfaces have full support
Semyon Dyatlov, Long Jin
We show that each limiting semiclassical measure obtained from a sequence of eigenfunctions of the Laplacian on a compact hyperbolic surface is supported on the entire cosphere bun…
Fractal Weyl laws and wave decay for general trapping
Semyon Dyatlov, Jeffrey Galkowski
We prove a Weyl upper bound on the number of scattering resonances in strips for manifolds with Euclidean infinite ends. In contrast with previous results, we do not make any stron…
Dolgopyat's method and the fractal uncertainty principle
Semyon Dyatlov, Long Jin
We show a fractal uncertainty principle with exponent , , for Ahflors-David regular subsets of of dimension . This improves over the volume bo…