Math 570: Teichmüller Theory and Geometric Structures

David Dumas

University of Illinois at Chicago
Spring 2013

cp1 structures
A holomorphic family of complex projective structures on a punctured torus. The black regions represent structures with quasi-Fuchsian holonomy.   (more images)

General information

Instructor David Dumas (
Office hours Monday 11-12 and Wednesday 12:30-1:30
CRN 34260
Lectures MWF 2:00 - 2:50pm in Taft Hall 313
Texts Complex projective structures, a chapter from the Handbook of Teichmüller Theory. (EMS Publishing House, 2009)
C. McMullen, Riemann Surfaces, Dynamics, and Geometry (Graduate lecture notes)
R. Benedetti and C. Petronio, Lectures on Hyperbolic Geometry. (Springer, 1992)
W. Goldman, Locally homogeneous geometric manifolds, from the proceedings of the 2010 International Congress of Mathematicians. (World Scientific, 2011)
J. H. Hubbard, Teichmüller Theory, vol. 1. (Matrix Editions, 2006)
F. Labourie, Lectures on Representations of Surface Groups. (Graduate lecture notes)
O. Lehto, Univalent Functions and Teichmüller Spaces. (Springer, 1987)
W. P. Thurston, Geometry and Topology of 3-Manifolds (Graduate lecture notes)

Course description

In this course we will discuss several types of geometric structures on surfaces and their deformation theories, emphasizing how complex-analytic and geometric aspects of these theories interact. Complex structures, hyperbolic structures, and complex projective (CP1) structures will be discussed in detail.

The course is intended for graduate students who have completed a complex analysis course (e.g. math 535) and a first course in differential geometry (e.g. math 549) at the graduate level.

The final list of topics to be covered may be altered somewhat to accommodate the interests of the students in the course and the pace that suits their common mathematical background. A tentative syllabus follows.

Course materials

Up: Home page of David Dumas