Symplectic Geometry

Catalog description

Symplectic geometry is a branch of differential geometry which studies manifolds endowed with a nondegenerate closed 2-form. The field originated as the mathematics of classical (Hamiltonian) mechanics, and it has connections to (at least!) complex geometry, algebraic geometry, representation theory, and mathematical physics. In this introduction to symplectic geometry, the class will begin with linear symplectic geometry, discuss canonical local forms (Darboux-type theorems), and examine related geometric structures including almost complex structures and Kähler metrics. Further topics may include symplectic and Hamiltonian group actions, the orbit method, the topology and geometry of momentum maps, toric symplectic manifolds, Hamiltonian dynamics, symplectomorphism groups, and symplectic embedding problems.