# Zeroes of Laplace eigenfunctions

 Mathematical Conversations Topic: Zeroes of Laplace eigenfunctions Speaker: Aleksandr Logunov Affiliation: Member, School of Mathematics Date: Wednesday, January 24 Time/Room: 6:00pm - 7:00pm/White-Levy

The classical Liouville theorem claims that any positive harmonic function in $R^n$ is a constant function. Nadirashvili conjectured that any non-constant harmonic function in $R^3$ has a zero set of infinite area. The conjecture is true and we will discuss the following principle for harmonic functions: "the faster the function grows the bigger the area of its zero set is". After that we will talk about the Yau conjecture on zeroes of Laplace eigenfunctions.