September 16th Malavika Mukundan (BU)
Title: On PSF branched self-covers of the plane
Abstract: In this talk we will start with this simple question: which branched self-covers of the plane are holomorphic? We will focus on a class of branched covers that satisfy the post-singular finiteness (PSF) property, and consider again the question of when such maps are holomorphic. Such maps are known to have vital importance in complex dynamics, and we will explore this connection.
September 23rd Karol Bacik (MIT)
Title: Hidden order in chaotic crowds
Abstract: At first glance, a crowd of pedestrians crossing a busy plaza may seem disordered, but if you look closely, you can discover hidden patterns. For example, two groups moving in opposite directions on a crosswalk spontaneously segregate into contraflowing lanes. In my talk, I will introduce a new kinetic theory that gives insight into the physical origin of lane formation and predicts some new dynamical phenomena. Mathematically, the discussion will amount to a sequence of stability problems of increasing complexity. To complement the theoretical analysis, I will also discuss a suite of experiments with human crowds - pretty videos of people wearing little paper hats will be provided.