Title: Many faces of Renormalization
Speaker: Misha Lyubich, Stony Brook
Date: Tuesday, February 24, 2015
Time: 01:00pm – 02:00pm
Place: Lecture Hall 102, Simons Center
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Abstract: Renormalization is a central idea of contemporary Dynamical Systems Theory, adapted from Statistical Physics and Quantum Field Theory. It allows one to control small scale structure of certain classes of systems, which leads to universal features of the phase and parameter spaces. We review several occurancies of Renormalization in Dynamics: for unimodal, quadratic-like, circle, Siegel, and parabolic maps that enlighten the structure of many Julia sets and the Mandelbrot set. In particular, we will show how it helps to construct Julia sets of positive area. If time permits, we mention one interplay between Dynamics and StatPhysics Renormalization that allows one to describe distribution of Lee-Yang zeros for the Hierarchical Diamond Ising model.