Dynamics and Moduli Spaces
Math 272 - Tu Th 10-11:30 - Science Center 507
Harvard University - Fall 2012
Curtis T McMullen
Intended for advanced graduate students.
- Various lecture notes and papers.
- 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.
- 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.
An introduction to the theory of conformal dynamical systems,
Riemann surfaces and their moduli spaces.
Topics may include:
Enrolled students should attend the course regularly.
Homework may be requested for those requiring
- Conformal dynamics
- Rational maps and Kleinian groups
- The thermodynamic formalism
- 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
| 4 Sept (Tu) || First class
| 24 Nov (Th) || Thanksgiving -- no class
| 4 Dec (Tu) || Last class