Riemann Surfaces and Hyperbolic Geometry

Math 275 - MWF 12-1 pm - Science Center 216
Harvard University - Fall 2009

Instructor: Curtis T McMullen

Suggested Texts
  • J. H. Hubbard, Teichmüller Theory, vol. 1, Matrix Editions, 2006.
  • O. Lehto, Univalent Functions and Teichmüller Spaces, Springer-Verlag, 1987
  • Matsuzaki and Taniguchi, Hyperbolic Manifolds and Kleinian Groups, Oxford Science Publications, 1998
  • J. Milnor, Dynamics in One Complex Variable , Third Edition. Princeton University Press, 2006.
  • J. Ratcliffe, Foundations of Hyperbolic Manifolds, 2nd Edition. Springer, 2006.
  • W. P. Thurston, Three-dimensional Geometry and Topology, Princeton University Press, 1997.
Other useful references Prerequisites. Intended for advanced graduate students.

Description Fundamental results and topics in Teichmüller theory, hyperbolic 3-manifolds,
complex dynamics and the geometry of moduli space. Topics may include:
  • Random walks on Riemann surfaces
  • Fuchsian and quasifuchsian groups
  • Holomorphic quadratic differentials
  • Perspectives on Teichmüller theory
  • The mapping-class group
  • Moduli space and its compactifications
  • Curves in moduli spce
  • Iterated rational maps
  • Rational maps with given combinatorics
  • Kleinian groups and hyperbolic 3-manifolds
  • Mostow rigidity
  • Geometrization of 3-manifolds
Grades. Enrolled students should attend the course regularly.

2 Sept (W) First class
7 Sept (M) Labor day - no class
12 Oct (M) Columbus day -- no class
11 Nov (W) Veteran's day -- no class
27 Nov (F) Thanksgiving -- no class
2 Dec (M) Last class
4-11 Dec (Tu-F) Reading period

Course home page: http://math.harvard.edu/~ctm/math275