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.

arXiv commentSubmitted to Proceedings of the ICM 2014, 23 pages

References in corpus (14)

• From Symplectic Measurements to the Mahler Conjecture
• A remark on the Mahler conjecture: local minimality of the unit cube
• New obstructions to symplectic embeddings
• Symplectic embeddings into four-dimensional concave toric domains
• Recent progress on symplectic embedding problems in four dimensions
• Symplectic embeddings of 4-dimensional ellipsoids into cubes
• Ehrhart polynomials and symplectic embeddings of ellipsoids
• Elementary approach to closed billiard trajectories in asymmetric normed spaces
• Ellipsoid embeddings and symplectic packing stability
• Symplectic capacity and short periodic billiard trajectory
• The isotropic position and the reverse Santaló inequality
• Contact geometry and isosystolic inequalities
• Symplectic embeddings of polydisks
• Periodic billiard trajectories and Morse theory on loop spaces

Cited by in corpus (10)

• Symplectic embeddings and the lagrangian bidisk
• On the symplectic size of convex polytopes
• Mahler's conjecture for some hyperplane sections
• Entropies from coarse-graining: convex polytopes vs. ellipsoids
• The Viterbo's capacity conjectures for convex toric domains and the product of a $1$-unconditional convex body and its polar
• A symplectic approach to Schrödinger equations in the infinite-dimensional unbounded setting
• Quantization in Cartesian coordinates and the Hofer metric
• Quantum Polar Duality and the Symplectic Camel: a Geometric Approach to Quantization
• A Funk perspective on billiards, projective geometry and Mahler volume
• A class of new bi-invariant metrics on the Hamiltonian diffeomorphism groups