Lecturer:

Course Type:

PhD Course

Academic Year:

2020-2021

Period:

February-March

Duration:

40 h

Description:

**The main references shall be the course notes.**

**Prerequisite: complex analysis.**

**Course material:**

- Riemann surfaces: definition and examples;
- Holomorphic and meromorphic functions on Riemann surface;
- Compact Riemann surface: genus, monodromy, homology;
- Differentials on Riemann surface and integration:- Riemann bilinear relation;- Jacobi variety and Abel theorem;- Divisors and Riemann-Roch theorem;
- Jacobi inversion problem and theta functions.

**Exam:**You need to solve an exercise and give a seminar on an agreed topic.

**Starting period:**February

**Lecture notes:**https://people.sissa.it/~grava/teaching.html

Additional Material:

Research Group: