The first call for applications for the new edition of the PhD Program in Mathematics UC|UP (starting September 2018) will be open during January 02, 2018 - February 02, 2018
Symplectic linear algebra. Symplectic manifolds. Symplectomorphisms. Lagrangian submanifolds. Theorems of Darboux and Weinstein (lagrangian neighborhood). Hamiltonian vector fields. Brief introduction to Poisson manifolds. Hamiltonian actions and moment map. Noether Theorem. Equivariance of the moment map and coadjoint orbits. Convexity Theorem. Symplectic reduction. Additional topics: Almost complex structures. Kähler manifolds. Contact manifolds. Lie algebroids and Poisson geometry. Toric symplectic manifolds.