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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). Fixing an arbitrary sub-Laplacian, some of our results hold for any eigenfunction, and others hold when averaging over random linear combinations of eigenfunctions. 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.

Room: 4336-4384 Pavillon Andr茅-Aisenstadt, Universit茅 de Montr茅al

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Meeting ID: 831 1853 9851

Passcode: 215516