MathematicsMATH 248 Symplectic Geometry

Basic definitions. Darboux theorem. Basic examples: cotangent bundles, Kähler manifolds and co-adjoint orbits. Normal form theorems. Hamiltonian group actions, moment maps. Reduction by symmetry groups. Atiyah-Guillemin-Sternberg convexity. Introduction to Floer homological methods. Relations with other geometries including contact, Poisson, and Kähler geometry.


Prerequisite(s): MATH 204; MATH 208 and MATH 209 are recommended as preparation. Enrollment is restricted to graduate students.