Title: Symplectic Geometry

Description: Hamilton’s equations and their physical origin, symplectic manifolds and various submanifolds, Moser arguments including Darboux theorem and Moser neighborhood theorems, contact manifolds, contact hypersurfaces, symplectizations, Legendrian front diagrams, topological Legendrian knot invariants, almost complex structures compatible with symplectic form, Hamiltonian group actions and symplectic reduction, symplectic toric manifolds, h principle with emphasis on holonomic approximation theorem along with applications to symplectic and contact geometry, Gromov non squeezing theorem and a summary of pseudoholomorphic curve theory.

Prerequisite: MAT 531

Credits: 3

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