Lie groupoids and the minimal domain of the Laplace operator on almost-Riemannian manifolds

Abstract: Lie groupoids are objects that are used in various branches of mathematics as desingularisations of singular objects. They come with an array of useful analytic tools, such as an associated pseudo-differential calculus, convolution and C*-algebras. One can use those tools to answer purely analytic questions about compatible differential operators. In the talk I will explain how one can use them to find minimal domains of singular differential operators and, in particular, how to find minimal domains of perturbations of the Laplace-Beltrami operator on 2D almost-Riemannian manifolds even in the presence of the tangency points.

analysis of PDEsdifferential geometrymetric geometryoptimization and controlspectral theory

Audience: researchers in the topic

( paper | video )

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Sub-Riemannian Seminars

Series comments: The "Sub-Riemannian seminars" are the union of the "Séminaire de géométrie et analyse sous-riemannienne" (held in Paris since 2011) and the "International Sub-Riemannian Seminars", which were born in spring 2020 as a reaction to the COVID-19 pandemic.

The new format will gather every 3 weeks on average, alternating between these types of sessions:

- physical session in Paris (Laboratoire Jacques-Louis Lions), also transmitted online on Zoom.

- fully online session on Zoom.

- special session hosted physically somewhere else, and transmitted online.

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