Syllabus
Topics in Conformal Dynamics
Math 275  Tu Th 10:0011:30 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 ,
SpringerVerlag, 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, BersRoyden 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 noinvariantline fields conjecture
 BrannerHubbard 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
