Iosif Polterovich, Université de Montréal

The sloshing problem is a Steklov type eigenvalue problem describing small oscillations of an ideal fluid. We will give an overview of some latest advances in the study of Steklov and sloshing spectral asymptotics, highlighting the effects arising from corners, which appear naturally in the context of sloshing. In particular, we will discuss the proofs of the conjectures posed by Fox and Kuttler back in 1983 on the asymptotics of sloshing frequencies in two dimensions. We will also outline an approach towards obtaining sharp asymptotics for Steklov eigenvalues on polygons. The talk is based on a joint work with M. Levitin, L. Parnovski and D. Sher.