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.