| Credits |
8 credit points |
| Instructors |
Heckman, G.J. (Radboud Universiteit Nijmegen) |
| E-mail |
g.heckman@science.ru.nl |
| Aim |
The student acquires a basic knowledge in symplectic geometry, with an open eye towards applications in physics and algebraic geometry. |
| Description |
In the first part of the course we will discuss symplectic manifolds, the standard examples of cotangent bundles, coadjoint orbits and complex projective manifolds. Next we treat Hamiltonian actions of Lie groups on symplectic manifolds, and discuss the symplectic reduction technique and geometric aspects of the moment map. Finally we treat applications in GIT (Guillemin-Sternberg), gauge theory (Hitchin) and Teichmueller theory (Mirzakhani). |
| Organization |
2 hours class per week |
| Examination |
Exercises plus oral exam. |
| Literature |
J.J. Duistermaat, Symplectic Geometry, Notes on the website of Duistermaat. G.J. Heckman and P. Hochs, Geometry of the momentum map, Notes on the website of Heckman. V. Guillemin and S. Sternberg, Symplectic techniques in physics, CUP, 1984. |
| Prerequisites |
Basic knowledge of manifolds and Lie groups. |
| Remarks |
The student taking this course is strongly advised to also take the course in Lie groups offered in the same fall. |
