Intended for graduate students. Prerequesites include algebraic topology, complex analysis and differential geometry on manifolds. This course will cover fundamentals of the theory of compact Riemann surfaces from an analytic and topological perspective. Automorphic forms Univalent functions, Bers embedding, Weil-Petersson metric Selberg trace formula Complex tori and K3 surfaces Reading and Lectures.
Students are responsible for all topics covered in the readings and lectures.
Lectures may go beyond the reading, and not every topic in the reading will be covered in class. Graduate students who have passed their quals are excused from a grade for this course. Grades for other students will be based on homework and a final project. Homework will be assigned every few weeks. Collaboration between students is encouraged, but you must write your own solutions, understand them and give credit to your collaborators.