The goal of this program is to bring together researchers in complex dynamics, arithmetic dynamics, and related fields, with the purpose of stimulating interactions, promoting collaborations, making progress on fundamental problems, and developing theoretical and computational foundations on which future work will build. Complex dynamics is the study of iteration of holomorphic self-maps of a complex space. Fundamental examples of such maps arise as algebraic self-maps of algebraic varieties. Starting with the fundamental results of Fatou and Julia, complex dynamics has evolved into a well established field with many deep theorems and many important unresolved questions. Arithmetic dynamics refers to the study of number theoretic phenomena arising in dynamical systems on algebraic varieties. Many global problems in arithmetic dynamics are analogues of classical problems in the theory of Diophantine equations or arithmetic geometry, including for example uniform bounds for rational... (more)

Kinetic theory plays a central role in many areas of mathematical physics, from nanoscales to continuum mechanics. It is an indispensable tool in the mathematical description of applications in physical and social sciences, from its origin in dilute gases, to wide applications such as semi-conductors, polymers, cells, plasma, galaxies, traffic networking, and swarming. The number of particles is typically more than 10²⁰.

On the one hand, kinetic models provide more detailed and accurate description of regimes where hydrodynamic equations are either invalid or simply not available. On the other hand, because modern computers are still inadequate in simulating the molecular or even quantum dynamics in emerging industrial needs in micro- and nanotechnology, kinetic equations provide models that can capture important features of microscopic or quantum phenomena with a manageable computational cost. Kinetic theory is at the core of multiscale modeling, which connects fundamental... (more)