HU Credits:
3
Degree/Cycle:
2nd degree (Master)
Responsible Department:
Mathematics
Semester:
2nd Semester
Teaching Languages:
Hebrew
Campus:
E. Safra
Course/Module Coordinator:
Dr. Shaul Zemel
Coordinator Office Hours:
By appointment
Teaching Staff:
Dr. Shaul Zemel
Course/Module description:
In the course we shall study what are Riemann surfaces, and the basic theory of functions and differentials on them. We shall get acquainted with the classical results in the compact case, like the RiemannHurwitz Formula, Abel's Theorem, the Jacobi Inversion Theorem, and the RiemannRoch Theorem. In addition, we shall present some results about the classification of Riemann surfaces, and we shall analyze their automorphism groups.
Course/Module aims:
The course aims to introduce the basic notions from the theory of Riemann surfaces, which today make the language which researchers in various mathematical domains use (e.g., Algebraic Geometry).
Learning outcomes  On successful completion of this module, students should be able to:
Find the genus of the Riemann surface associated with an algebraic curve
Determine the field of meromorphic functions on a branched covering of the sphere
Find a basis for the differentials that is adapted to a point on a concrete Riemann surface
Find relations of linear equivalence between divisors on Riemann surfaces
Evaluate the automorphism group of a given Riemann surface
Attendance requirements(%):
0
Teaching arrangement and method of instruction:
Lectures
Course/Module Content:
Riemann surfaces, holomorphic maps, differentials, meromorphic functions, canonical homology bases, Riemann bilinear relations, RiemannRoch Theorem, linear equivalence, Abel's Theorem, Jacobi Inversion Theorem, projective embeddings, simply connected Riemann surfaces, fundamental group, Kleinian groups, Fuchsian groups, automorphisms
Required Reading:
None
Additional Reading Material:
I shall follow some chapters of the book "Riemann Surfaces" by Farkas and Kra
Course/Module evaluation:
End of year written/oral examination 0 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 100 %
Assignments 0 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 0 %
Additional information:
Edmund Safra Campus
