The program will aim to give a broad prospective of application of renormalization ideas. The concentration will be in the areas where renormalization and scaling invariance led to important recent progress, such as one-dimensional dynamics (real and complex), 2D conformal invariance, geometric PDEs, and their connection to the underlying physics ideas. The purpose is two-fold: to survey the recent achievements and outline new directions of research on the one hand; and to foster the interaction between various branches of the dynamics and mathematical physics communities working in renormalization.

The first half of the program will concentrate on the physical aspects of renormalization: statistical physics, conformal field theory, the underlying Hopf-algebraic structure, renormalization in PDE. The second half will have the dynamical flavour: holomorphic and smooth dynamics; KAM theory and renormalization of Hamiltonian flows; conformal invariance and universality in 2D stochastic processes. We also plan to touch on the recent breakthrough in the Geometrization Program based on the dynamics of the Ricci Flow and its connection to the concept of renormalization. The program will include two workshops: one in September-October, focused on mathematical physics, and one in December, focused on Dynamics. There will be a series of graduate courses and mini-courses on topics including:

• Renormalization in one-dimensional dynamics;
• Renormalization in infinite-dimensional dynamical systems;
• Renormalization in mathematical physics;
• Renormalization in Hamiltonian systems;
• Hopf-algebraic aspects of renormalization;
• Percolation, Brownian motion, and SLE.