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# Cyril Letrouit (MIT) – Nodal sets of eigenfunctions of sub-Laplacians

## March 29, 2023 @ 3:00 pm - 4:00 pm

Mode: In-Person

Title: *Nodal sets of eigenfunctions of sub-Laplacians*

Abstract: Nodal sets of eigenfunctions of elliptic operators on compact manifolds have been studied extensively over the past decades. In a recent work, we initiated the study of nodal sets of eigenfunctions of hypoelliptic operators on compact manifolds, focusing on sub-Laplacians (e.g. on compact quotients of the Heisenberg group). Our results show that nodal sets behave in an anisotropic way which can be analyzed with standard tools from sub-Riemannian geometry such as sub-Riemannian dilations, nilpotent approximation and desingularization at singular points. This is a joint work with S. Eswarathasan.