36 citations · 36 across the 2 of their papers we have counts for
6 papers
Around quantum ergodicity
Semyon Dyatlov
We discuss Shnirelman's Quantum Ergodicity Theorem, giving an outline of a proof and an overview of some of the recent developments in mathematical Quantum Chaos.
An introduction to fractal uncertainty principle
Semyon Dyatlov
Fractal uncertainty principle states that no function can be localized in both position and frequency near a fractal set. This article provides a review of recent developments on t…
Microlocal analysis of forced waves
Semyon Dyatlov, Maciej Zworski
We use radial estimates for pseudodifferential operators to describe long time evolution of solutions to where is a self-adjoint 0th order pseudodifferent…
Notes on hyperbolic dynamics
Semyon Dyatlov
These expository notes present a proof of the Stable/Unstable Manifold Theorem (also known as the Hadamard--Perron Theorem). They also give examples of hyperbolic dynamics: geodesi…
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:…
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,…