Lecturer:
Course Type:
PhD Course
Academic Year:
2021-2022
Period:
February-April
Duration:
40 h
Description:
- Riemann surfaces: definitions 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
- Integrable systems: the Toda Lattice with periodic boundary conditions
- Integrable systems with random initial data and connection with the theory of random matrices
The main references shall be the course notes.
Exam: You need to solve an exercise and give a seminar on an agreed topic.
Prerequisites:
Complex analysis
Basic topology
Research Group:
Location:
A-136