Title: Dynamics, Mixing, and Coherence

Abstract: Coherent regions in geophysical flows play fundamental roles by organising fluid flow and obstructing transport. For example, in the ocean, coherence impacts dynamics from global scales down to scales of at least tens of kilometres, and strongly influences the transportation of heat, salt, nutrients, phytoplankton, pollution, and garbage. I will describe some recent mathematical constructions, ranging across dynamical systems, probability, and geometry, which enable the accurate identification and tracking of such structures, and the quantification of associated mixing and transport properties. I will also present case studies from a variety of geophysical settings.