Geometry, duality and odd transport in flatland

Effective theories are very useful to extract transport properties at long wavelengths, which can be done by studying the response to external sources and geometric deformations. In two dimensions one can also take advantage of particle-vortex duality which allows a similar description for Quantum Hall states and superfluids/superconductors using statistical gauge fields. I will discuss the effective theory description of two-dimensional states with broken parity and time-reversal invariance and the relation between odd transport and symmetry and topological properties of the state.