David Dumas
University of Illinois at Chicago
Spring 2013
A holomorphic family of complex projective structures on a punctured torus. The black regions represent structures with quasi-Fuchsian holonomy. (more images) |
Instructor | David Dumas (ddumas@math.uic.edu) |
---|---|
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) |
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.