Abstract:

Given a point $x$ on a Schubert variety, how does one determine whether or not $x$ is singular? I plan to review some aspects of this well-studied problem that revolve around a celebrated criterion due to Carrell and Peterson. It reduces the problem to a combinatorial study of a certain "Bruhat graph".

The talk is intended as a brief survey for non-experts of more or less classical material. Time permitting, I shall however touch upon some recent developments concerning closures of symmetric orbits towards the end.