Topics in Conformal Dynamics

Math 275 - Tu Th 10:00-11:30 pm - 112 Science Center
Harvard University - Fall 2001

Instructor: Curtis T McMullen (

  • 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.

  • 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

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