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# Iosif Polterovich, Universite de Montreal – Analysis & PDE Seminar

## April 18, 2018 @ 4:00 pm - 5:00 pm

**Title:** Isoperimetric inequalities for Laplace eigenvalues on surfaces: some recent developments

**Abstract: **Isoperimetric inequalities for Laplace eigenvalues have a long history, going back to the celebrated Rayleigh-Faber-Krahn inequality for the fundamental tone. Still, many basic questions remain unanswered, particularly, for higher eigenvalues. In the talk I will give an overview of some recent developments in the study of isoperimetric inequalities for eigenvalues on compact surfaces with a Riemannian metric. In particular, I will discuss a solution of a conjecture posed by N. Nadirashvili in 2002 regarding the maximization of higher Laplace-Beltrami eigenvalues on the sphere.

The talk is based on a joint work with M. Karpukhin, N. Nadirashvili and A. Penskoi.