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.