Dynamics and Moduli Spaces

Math 272 - Tu Th 10-11:30 - 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. 187--188, 1990.
  • Foundations of Hyperbolic Manifolds. J. G. Ratcliffe, Springer-Verlag, 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 Rn
  • Moduli spaces of Riemann surfaces
  • Moduli spaces of dynamical systems
  • The Teichmüller geodesic flow
  • Compactification by R-trees
Grades. Enrolled students should attend the course regularly. Homework may be requested for those requiring letter grades.

4 Sept (Tu) First class
24 Nov (Th) Thanksgiving -- no class
4 Dec (Tu) Last class

Course home page: http://math.harvard.edu/~ctm/math272