Session S33 - Spectral Geometry

Monday, July 12, 12:00 ~ 12:20 UTC-3

The Steklov spectrum, the boundary Laplacian and Hörmander’s rediscovered manuscript

Iosif Polterovich

Université de Montréal, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

How close is the Dirichlet-to-Neumann map to the square root of the corresponding boundary Laplacian? This question has been actively investigated in recent years. Somewhat surprisingly, a lot of techniques involved can be traced back to a newly rediscovered manuscript of Lars Hörmander from the 1950s. We present Hörmander’s approach and its applications, with an emphasis on the asymptotics for Steklov eigenvalues.

Joint work with Alexandre Girouard (Université Laval), Mikhail Karpukhin (Caltech) and Michael Levitin (University of Reading).

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