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Explore the mathematical theory of invariant distances on Legendrian spaces in this advanced symplectic geometry lecture from the Institute for Advanced Study. Delve into the motivation behind studying invariant distances on spaces of Legendrians before examining two fundamental results: the construction of a new unbounded invariant distance on the universal cover of many Legendrian isotopy classes, and the discreteness of any invariant distance on Legendrian isotopy classes. Discover how the first result emerges from contact rigidity principles while the second follows from contact flexibility theory. Learn from Pierre-Alexandre Arlove of the University of Strasbourg as he presents cutting-edge research in this specialized area of differential geometry and symplectic topology, providing insights into the geometric properties and structural characteristics of Legendrian submanifolds and their associated metric spaces.
