Riemann Surfaces and Hyperbolic Geometry
Math 275  MWF 121 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,
SpringerVerlag, 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,
Threedimensional Geometry and Topology,
Princeton University Press, 1997.
Other useful references
 M. B. Bekka and M. Mayer,
Ergodic theory and topological dynamics of group actions on homogeneous spaces,
Cambridge University Press, 2000.
 Benedetti and Petronio,
Lectures on Hyperbolic Geometry,
SpringerVerlag, 1992.
 B. Bollobas,
The asymptotic number of unlabelled regular graphs
 E. Ghys, Dynamique des flots unipotents sur les espaces homogènes,
Sem. Bourbaki 1991/92; Asterisque 206.
 M. Gromov,
Volume and bounded cohomology
 I. Kapovich and N. Benakli,
Boundaries of hyperbolic groups
 S. Kerckhoff,
The Nielsen Realization Problem
 C. McMullen,
From dynamics on surfaces to rational points on curves.
 C. McMullen,
Notes on Teichmüller Theory and Complex Dynamics
 C. McMullen,
Notes on Ergodic Theory
 G. Mess,
Lorentz spacetimes of constant curvature
(see Prop. 22 for the Earthquake Theorem).
 C. Series,
Martin boundaries of random walks on Fuchsian groups
 W. P. Thurston,
Geometry and Topology of 3Manifolds.
Prerequisites.
Intended for advanced graduate students.
Description
Fundamental results and topics in Teichmüller theory, hyperbolic
3manifolds,
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 mappingclass group
 Moduli space and its compactifications
 Curves in moduli spce
 Iterated rational maps
 Rational maps with given combinatorics
 Kleinian groups and hyperbolic 3manifolds
 Mostow rigidity
 Geometrization of 3manifolds
Grades.
Enrolled students should attend the course regularly.
Calendar.
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 
411 Dec (TuF)  Reading period 
