Title: “Fractal geometry methods in semiclassical quantum chaos”

Abstract: Quantum Chaos broadly speaking studies the relationship between classical chaos theory and the corresponding quantum dynamics described by the Schrödinger equation. Fractals play a major role in describing the statistics of classically chaotic systems, and in the past decades fractal geometry has seen some major breakthroughs bringing together tools from additive combinatorics, harmonic analysis and geometric measure theory. As classical chaos is expected to be reflected in the semiclassical limits of quantum chaotic models, bringing some of these new ideas to quantum chaos has become an active study in the past years, in particular after the introduction of Fractal Uncertainty Principle in the work of Dyatlov and Zahl in 2016.

In this introductionary talk I will give a bird’s-eye view of this progress and some of the current challenges the field faces. We then discuss our recent work in adapting these ideas in intermittent systems with mixed phase space of integrable and chaotic components.