Analysis on singular and non-compact spaces and Lie manifolds

Abstract: I will begin by reviewing some classical results on the analysis on compact manifolds and on manifolds with conical points (due to Kondratiev and others). It turns out that many of these classical results generalize to a larger class of singular or non-compact spaces defined using Lie algebroids and Lie manifolds. Since we will treat singular spaces by blowing them up to a non-compact manifold, I will refer in the following only to non-compact manifolds.

In order to obtain the mentioned generalizations, I will stress the role of Lie algebroids and hence of suitable classes of vector fields in modelling the geometry at infinity, which is at the heart of the definition of a Lie manifold. As an example, I will explain how to obtain Fredholm conditions for the natural operators on suitable Lie manifolds. The results of this talk are based, in part, on joint work with Ammann, Carvalho, and Yu.

mathematical physicsanalysis of PDEsdifferential geometryspectral theory

Audience: researchers in the discipline

Analysis and Differential Geometry International Seminar @ Aveiro

Series comments: The online seminar Analysis and Differential Geometry International Seminar (ADGIS@Aveiro) aims to bring together specialists from analysis and geometry with particular emphasis on partial differential equations, differential geometry, analysis on filtered manifolds, singular (differential) operators, spectral theory, and their connections to other fields.

In order to register and receive a link to the talks please contact one of the organizers.