|Topic:||Zeroes of Laplace eigenfunctions|
|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.