Anomalous hydrodynamics in condensed matter systems*

Fluid dynamics is a powerful tool in studying both quantum and classical many body systems. I will review recent progress in using fluid dynamics to describe two-dimensional isotropic fluids with broken parity. The viscous stress tensor for these fluids can possess an anomalous part known as odd or Hall viscosity. This peculiar viscosity does not lead to any dissipation in the fluid. Examples of fluids with odd viscosity include rotating superfluids, plasmas in magnetic fields, quantum Hall fluids, and chiral active fluids. I will describe some manifestations of the odd viscosity. In particular, I will focus on surface waves propagating along the boundaries of such fluids.