Steklov eigenvalues, sloping beaches, and quantum graphs

Steklov eigenvalues, sloping beaches, and quantum graphs

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Iosif Polterovich, University of Montreal

Zoom link: https://princeton.zoom.us/j/594605776

The Steklov eigenvalue problem has recently become one of the central topics in spectral geometry. I will overview some latest advances in the subject, with an emphasis on spectral asymptotics for domains with corners. This problem is closely linked to some old questions in hydrodynamics, as well as to the study of quantum graphs. Applications to the inverse spectral problem will also be discussed.

The talk is based on the results obtained in collaboration with Michael Levitin, Leonid Parnovski, David Sher, and Stanislav Krymski.