MATH777 MODULI SPACES OF CURVES
| Course Code: | 2360777 |
| 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. ALİ ULAŞ ÖZGÜR KİŞİSEL |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
Upon successful completion of this course, a student is expected to understand the various viewpoints for constructing the moduli spaces of algebraic curves of a given genus, and the compactifications of these moduli spaces.
Course Content
Understanding the behavior of families of algebraic curves is of central interest in many branches of mathematics, including algebraic geometry, mathematical physics, low dimensional topology, as well as certain branches of theoretical physics such as string theory and various gauge theories. Moduli spaces of algebraic curves are among the standard tools for researchers working in these areas. The course aims to cover the essentials of the subject and bring the students to a position so that they can access the modern literature.
Course Learning Outcomes
By the end of the course a succesful student will
- Understand various definitions of a moduli space
- Construct and make computations with different compactifications of moduli spaces.
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