Syllabus
Topics in Conformal Dynamics
Math 275 - Tu Th 10:00-11:30 pm - 112 Science Center
Harvard University - Fall 2001
Instructor:
Curtis T McMullen
(ctm@math.harvard.edu)
Texts
- Tan Lei, The Mandelbrot Set, Theme and Variations , Cambridge University Press, 2000.
- Matsuzaki and Taniguchi, Hyperbolic Manifolds and Kleinian Groups , Oxford Science Publications, 1998.
- J. Milnor, Dynamics in One Complex Variable , Vieweg, 1999.
- O. Lehto, Univalent Functions and Teichmueller spaces , Springer-Verlag, 1987.
Useful references
- McMullen, Complex Dynamics and Renormalization , Princeton University Press, 1994.
Prerequisites.
Intended for advanced graduate students.
Topics.
Advanced methods in complex dynamics, hyperbolic geometry,
Kleinian groups and Teichmueller theory.
Topics may include:
- Holomorphic motions, Bers-Royden extension
- Stability of rational maps and Kleinian groups
- Thurston's characterization of rational maps
- Iteration on Teichmueller space
- Rigidity of algebraic families; solving polynomials
- The Teichmueller space of a rational map
- The no-invariant-line fields conjecture
- Branner-Hubbard tableau, measure zero Julia sets
- Yoccoz puzzles, local connectivity
- Pleated surfaces, measure zero limit sets
- Hyperbolic reflection groups
Grades.
Students who need a letter grade for the course are invited to
write a final paper, due Monday, 7 January.
Calendar.
- Thu, 13 Sep. First class
- Thu, 22 Nov. No class - Thanksgiving
- Thu, 13 Dec. Last class
- Wed 2 Jan. Reading period begins
- Mon 7 Jan. Final papers for this course due
- Fri 12 Jan. Reading period ends