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Interpolation inequalities in sub-Riemannian geometry: an overview

Luca Rizza
Institution: 
CNRS
Schedule: 
Tuesday, October 20, 2020 - 15:00
Location: 
A-005
Location: 
A-005 and Zoom, sign in to get the link
Abstract: 

Sub-Riemannian manifolds are metric spaces that model systems with non-holonomic constraints, and constitute a vast generalization of Riemannian geometry. They arise in several areas of mathematics, including control theory, subelliptic PDEs, harmonic and complex analysis, geometric measure theory and calculus of variations. In the last 10 years, a surge of interest in the study of geometric and functional inequalities on sub-Riemannian spaces revealed unexpected behaviours and intriguing phenomena that failed to fit into the classical schemes inspired by Riemannian geometry. In this talk I will review some recent developments on the subject, focusing on the topic of interpolation inequalities for optimal transport and comparison geometry of these structures.

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