Feng Luo
Complex Analysis II
This is a continuation of Prof. Matveev’s course on complex analysis (Math 503). Complex analysis is a cornerstone of mathematics. The intuitive geometric underpinnings of complex analysis leads to Riemann surface theory. The theory is a source in mathematics and you can learn and trace many of the original ideas in current mathematical research come from it. The course will be an intermediate level introduction to Riemann surface theory and will 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
4. Riemannian metrics and hyperbolic geometry
5. Riemann-Roch, Abel and Jacobi theorems
6. The Uniformization theorem and its applications.
If you have any questions about the topics, please contact: fluo@math.rutgers.edu
There will be no text books for the class. The main references are
[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
Math 503 Complex Analysis, Math 501 Real Analysis and Point Set Topology