Dynamics of braid groups and slicings

The braid group B_n on n strands is an important mathematical object with interesting connections to many pure and applied areas, such as fluid mixing, physics, topology and representation theory. Accordingly, one can study B_n from a variety of perspectives. For example, algebraically the Burau representation of B_n has applications in knot theory and symplectic topology. Dynamically, the realisation of B_n as the mapping class group of the punctured disc leads to the study of entropy of braids. It is an interesting question how to link these two approaches. In this talk we'll explain some results in this direction which link dynamical properties of braids to new structures in homological algebra arising from the categorical Burau representation. Based on ongoing work with Ed Heng (IHES) and Tony Licata (ANU).