The major goal of the semester is to bring together experts and young researchers to initiate new interactions on various aspects of two main topics: chaotic dynamical systems in and out of equilibrium on the one hand, and the geometry of non-conformal systems on the other hand. A characteristic feature of chaotic dynamics is the emergence of various fractal objects in these systems. Discovering further connections between the two main themes of the semester has great potential.
Statistical physics is a mathematical framework originating from the 19th century that applies statistical methods and probability theory to large assemblies of microscopic entities (atoms, molecules,...) to explain macroscopic properties like temperature, pressure, diffusion of heat, etc.. In order to solve these problems, the 20th century saw first the development of modern probability theory, and later the theory of hyperbolic dynamical systems that applies the laws of Newtonian mechanics. In the modern setting, the goal is to understand processes where the governing laws change in time (like the influence of global warming), and patterns that stay on for a while even if their environment is chaotic.
Considerable attention has been paid, and several breakthrough results have emerged in recent years in geometric measure theory and dimension theory of iterated function systems using, for example, algebraic combinatorics and Fourier analysis. However, many questions remain open regarding the dimension, geometric, and measure-theoretic properties of conformal and, especially, non-conformal attractors and stationary measures.