Title: Nodal sets for eigenfunctions of sub-Laplacians

Abstract: The study of zero sets (or so-called nodal sets) of functions is a common one in various areas of mathematics and there is a long tradition, particularly in PDE, focusing on that of eigenfunctions of Laplacians.  However, very little if anything, has been said about nodal sets for solutions of hypoelliptic equations, the latter occupying an important place in probability, control theory, et cetera.

In this talk, I will present joint work with Cyril Letrouit (MIT/CNRS-U. Paris-Saclay) on nodal sets for eigenfunctions of sub-Laplacians on compact manifolds, a prime example of hypoelliptic differential operators.  We will discuss an analogue of Courant's nodal domain theorem and the density of the nodal set as quantified through sub-Riemannian-geometric quantities.  While there are similarities with the paths in the classical proofs, we crucially use tools from hypoelliptic theory and sub-Riemannian geometry.