Fractal Uncertainty Principle and Quantum Chaos

Explore a 47-minute lecture on fractal uncertainty principle and quantum chaos presented by Semyon Dyatlov at the International Mathematical Union. Delve into the intricacies of classical/quantum correspondence and its limitations, examining results that rely on chaotic classical dynamics without classical counterparts. Discover key findings on Laplacian eigenfunctions, Schrödinger equation observability, and wave behavior on hyperbolic surfaces. Learn about the fractal uncertainty principle as a crucial tool in understanding quantum phenomena. Gain insights from collaborative research with renowned mathematicians, covering topics such as semiclassical measures, Arnold cat map, open quantum chaos, and spectral gaps. Access accompanying slides for visual support of complex mathematical concepts discussed throughout the presentation.

Intro
Overview
Control of eigenfunctions
An illustration
Applications to PDE
Semiclassical measures II
Main tool fractal uncertainty principle (FUP)
Main tool: fractal uncertainty principle (FUP)
A bit about proof of Theorem 1
Illustration: Arnold cat map
Open quantum chaos and resonances
Spectral gap
Higher dimensional FUP?