Matthew Finn School of Mathematical Sciences, The University of Adelaide Topological chaos in two and three dimensions Wednesday 21st April 14:05-14:55pm, New Law School Seminar 030 (Building F10). Research into two-dimensional laminar fluid mixing has enjoyed a renaissance in the last decade since the realisation that the Thurston–Nielsen theory of surface homeomorphisms can assist in designing efficient "topologically chaotic" batch mixers. In this talk I will survey some tools used in topological fluid kinematics, including braid groups, train-tracks, dynamical systems and topological index formulae. I will then make some speculations about topological chaos in three dimensions.