Contacts

Graduate Menu

Graduate Resources

Course Descriptions

16:640:504 - Theory of Functions of a Complex Variable II

Spring 2027

Feng Luo

Subtitle:

Complex variable II

Course Description:

This is a continuation of Math 503. The course will be an intermediate-level introduction to Riemann surface theory and focus on how it connects various disparate concepts from analysis, geometry, topology, and algebraic geometry.
Topics to be covered include:
1. Basic surface topology, Riemann surfaces, and holomorphic maps
2. Calculus on surfaces, algebraic curves, and algebraic functions
3. The Dirichlet problem and harmonic functions
6. Riemannian metrics and hyperbolic geometry
7. Riemann-Roch, Abel and Jacobi theorems
8. The Uniformization theorem and its applications.
There will be no textbooks. The following are good references:[1] Forster, Lectures on Riemann Surfaces, Springer-Verlag, 1981
[2] Donaldson, Riemann surfaces, Oxford Press, 2011
[3] Farkas and Kra, Riemann Surfaces, Springer-Verlag, 1991
[4] Ahlfors, complex analysis, McGraw-Hill Education; 3rd edition, 1979

Textbook:

none

Prerequisites:

point set topology, real analysis and complex analysis.

 

Schedule of Sections:

 16:640:504 Schedule of Classes

 

Previous Semesters: