Smooth Dynamics, Random Walks, and Fractal Geometry: New Connections and Directions

This conference brings together scholars from three vibrant fields of mathematics: smooth dynamical systems, random walks and homogeneous dynamics, and fractal geometry. While distinct, there are deep relations between them. A central unifying theme is rigidity: the notion that dynamically or arithmetically defined sets and measures exhibit irregular behavior only due to specific algebraic, geometric, or combinatorial obstructions. Another overarching theme is equidistribution, both its emergence in the absence of obstructions, and its powerful applications across disciplines. The event comes in response to a variety of recent breakthroughs at the interface of these areas. Its aim is to foster new interactions and collaborations among researchers working in these fields, sharing techniques, goals, and challenges.

Specific topics to be covered include: (1) the Fourier decay problem for stationary measures; (2) exponential mixing and effective equidistribution in random dynamical systems; (3) advances in effective unipotent dynamics; (4) recent developments in restricted projection theory, and its applications.