Dynamics and Moduli Spaces
Math 272  Tu Th 1011:30  Science Center 507
Harvard University  Fall 2012
Instructor:
Curtis T McMullen
Suggested Texts
 Various lecture notes and papers.
C. McMullen.
 Zeta Functions and the Periodic Orbit Structure of Hyperbolic Dynamics.
W. Parry and M. Pollicott. Asterisque, vol. 187188, 1990.
 Foundations of Hyperbolic Manifolds.
J. G. Ratcliffe, SpringerVerlag, 1994.
 Dynamics in One Complex Variable.
J. Milnor,
 Teichmüller Theory, vol. 1.
J. H. Hubbard.
 Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces.
T. Bedford, M. Keane, C. Series (eds.)
 Ergodic Theory.
I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai.
Prerequisites.
Intended for advanced graduate students.
Description.
An introduction to the theory of conformal dynamical systems,
Riemann surfaces and their moduli spaces.
Topics may include:
 Conformal dynamics
 Rational maps and Kleinian groups
 The thermodynamic formalism
 Billiards
 Algebraic curves in moduli space
 Mixing and unique ergodicity; unipotent and semisimple flows
 Moduli spaces of lattices in R^{n}
 Moduli spaces of Riemann surfaces
 Moduli spaces of dynamical systems
 The Teichmüller geodesic flow
 Compactification by Rtrees
Grades.
Enrolled students should attend the course regularly.
Homework may be requested for those requiring
letter grades.
Calendar.
4 Sept (Tu)  First class 
24 Nov (Th)  Thanksgiving  no class 
4 Dec (Tu)  Last class 
