Mathematical Conversations

Topic: Zeroes of Laplace eigenfunctions

Speaker: Aleksandr Logunov

Affiliation: Member, School of Mathematics

Date & Time: Wednesday January 24th, 2018, 6:00pm - 7:00pm

Location: 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.