When symplectic topology meets Banach space geometry

Abstract

In this paper we survey some recent works that take the first steps toward establishing bilateral connections between symplectic geometry and several other fields, namely, asymptotic geometric analysis, classical convex geometry, and the theory of normed spaces.

Submitted to Proceedings of the ICM 2014, 23 pages

References in corpus (3)

• Symplectic embeddings of 4-dimensional ellipsoids into cubes
• Symplectic embeddings of polydisks
• Periodic billiard trajectories and Morse theory on loop spaces

Cited by in corpus (3)

• The Viterbo's capacity conjectures for convex toric domains and the product of a $1$-unconditional convex body and its polar
• A class of new bi-invariant metrics on the Hamiltonian diffeomorphism groups
• A Funk perspective on billiards, projective geometry and Mahler volume