Course Information and Syllabus

445: Riemann Surfaces (Complex Geometry)

Please consult this course homepage for updates on the course schedule, texts, exercises, handouts...

Course title

Riemann Surfaces

Course number

Meeting times/Location

445

MWF 10  Lunt 101

Professor:

Office Hours

Steve Zelditch

M  11-12

Course description

compact Riemann surfaces. Instead one has twisted holomorphic functions--namely, holomorphic sections of line bundles and meromorphic functions. We will concentrate on holomorphic line bundles, their holomorphic

sections, and related kernel functions: the Szego (or Bergman) kernel, Green's functions, prime form. We will also study Hermitian metrics on line bundles and their curvature forms. Time permitting,

we may consider the entire space of Kahler metrics of fixed area on a Riemann surface  as an infinite dimensional symmetric space.

Pre-requisites:                                       

                                                                                            Some background on calculus on manifolds and holomorphic functions of one complex variable. Some PDE.

I will post and grade  exercises

Textbooks

There are many good Lecture series online. We will also use material from books.

2. D. Varolin, Riemann Surfaces by way of Analytic Geometry.

3. R. Narasimhan, {\it Compact Riemann surfaces.} Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel, 1992.
 

Other texts: O. Forster Riemann Surfaces. Farkas and Kra, Riemann Surfaces.