Dispersive PDE on noncompact symmetric spaces

Jean-Philippe Anker (Université d’Orléans)

12-Jan-2022, 17:00-18:00 (2 years ago)

Abstract: We consider the wave equation and the Schrödinger equation on general symmetric spaces of the noncompact type, which is an interesting class of Riemannian manifolds with nonpositive curvature, including all hyperbolic spaces. The standard strategy consists in establishing first pointwise kernel estimates for the fundamental solutions, in deducing next dispersive and Strichartz inequalities for the linear equations, and in applying them finally to semilinearities. This program was successfully achieved for various classes of manifolds over the past 40 years, in particular for hyperbolic spaces 10-15 years ago. We were recently able to extend it to symmetric spaces of higher rank, in collaboration with V. Pierfelice, S. Meda, M. Vallarino and H.-W. Zhang. In this talk, we shall report on these progresses, emphasizing on the tools used to tackle the higher rank case.

classical analysis and ODEsfunctional analysisrepresentation theoryspectral theory

Audience: researchers in the topic


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Organizers: Alessandro Monguzzi*, Valentina Casarino, Bianca M. Gariboldi, Stefano Meda
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