The idea of renormalization emerged in the 1960s in mathematical physics, and revolutionized the field of Statistical Mechanics, where it has become the main tool in the analysis of phase transitions and critical phenomena. In the 1970s, renormalization ideology was transferred to Dynamics due to independent discoveries of universality phenomena by Feigenbaum and Coullet & Tresser. It has since become one of the most powerful tools of understanding small scale structure of a large variety of dynamical systems. Renormalization has become particularly well (and rigorously) developed in the conformal context, in particular, in the geometric problems related to the celebrated MLC Conjecture on the local connectivity of the Mandelbrot set.

 

This workshop will bring together top experts in the study of renormalization in Dynamics to map out the current state of the art and the new directions in this exciting and rapidly developing field.