MATH748 SYMPLECTIC TOPOLOGY
| Course Code: | 2360748 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. SERGEY FİNASHİN |
| Offered Semester: | Spring Semesters. |
Course Objectives
At the end of the course the student will know
- basic notions, examples, and techniques about the symplectic topology, like canonical symplectic structure on the cotangent space, elements of Hamiltonian mechanics, symplectization.
- To know the basic structural results, like Darboux-Moser-Weinstein theorems
- some applications of symplectic topology to 4-manifolds, to have an idea about geography of symplectic manifold.
- To have a general knowledge about J-holomorphic curves, symplectic camel and capacities, Arnold Liouville theorem and Hamiltonian equations, the moment map.
Course Content
Darboux-Moser-Weinstein theorems, J-holomorphic curves. Symplectic camel and capacities. Symplectization and contactization. Arnold Liouville theorem and Hamiltonian equations. moment map and symplectic reduction. Kaehler manifolds and toric manifolds.
Course Learning Outcomes
Students should be able to apply in elementary examples (surfaces and some 4-manifolds) the basic technics listed in the course objectives.
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Gains academic maturity through self-study. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Carries out parts of a mathematical research program independently. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Gets exposed to academic culture through interaction with others. | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others. | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution