simplectic geometry

Type: Concept

As of November 2026, simplectic geometry has been mentioned in one podcast episode on Institute for Advanced Study (Dec 2025). A related mathematical field to contact geometry.

Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the Hamiltonian formulation of classical mechanics where the phase space of certain classical systems takes on the structure of a symplectic manifold.