Topological lasers and condensates.

Topological photonics aims to replicate fermionic symmetries as feats of precision engineering with the goal to obtain symmetry-protected modes. I discuss how to preserve the symmetry protection in the presence of gain, loss and nonlinearities, which are effects that do not have a direct electronic counterpart. This leads to a topological mechanism of mode selection that can be utilized in lasers, and the formation of compactons in flat-band condensates. Conceptually, a key ingredient in these applications is a non-hermitian version of charge-conjugation symmetry, which for electrons applies to superconductors.This symmetry naturally generalizes to systems with loss and gain, while in nonlinear settings it constitutes a dynamical symmetry, which also allows for time-periodic symmetry-protected modes.