## Speaker:

Eugenia Malinnikova

## Institution:

Stanford University

## Time:

Thursday, April 14, 2022 - 4:00pm

## Host:

## Location:

RH 306

A classical idea in the study of eigenfunctions of the Laplace-Beltrami operator is that they behave like polynomials of degree corresponding to the eigenvalue. We will discuss several properties of eigenfunctions which confirm this idea, including the Bernstein and Remez inequalities. As a corollary, we will formulate a local version of the celebrated Courant theorem on the number of nodal domains of eigenfunctions. The proofs of the inequalities rely of the frequency function of solution to elliptic PDEs. In the talk, we will also review some striking properties of this frequency function.