Course Page for Teichmuller Theory and Dynamical Systems at the CUNY Graduate Center
This course is taught by Jeremy Kahn, now at the CUNY Graduate Center.
The course notes are being written by Maxime Bourque.
The first two lectures are intended to be an overview, with brief sketches of proofs:
Lecture 1: Uniqeness for critically periodic folding maps of the interval
Lecture 2: Uniqueness and Existence for
post-critically finite rational maps
Lecture 3: Extremal length and quadratic differentials
Lecture 4: Quadratic differentials and Teichmuller's theorem
Lecture 5: Teichmuller's Uniqueness Theorem
Lecture 6: Some of the ideas for Teichmuller's Existence Theorem
Lecture 7: The general definition of K-qc mappings
Lecture 8 is taken out of Chapter 2 of Ahlfors' Lectures on Quasiconformal Mappings
Lecture 9: The proof of Teichmuller's Existence Theorem
Lecture 10: The Teichmuller Space
Lecture 11: The Bers embedding
Lecture 12: Combinatorial Rigidity of Post-critically Finite Rational Maps
Lecture 13: Thurston's iteration on Teichmuller space
Lecture 14: Why Thurston's iteration has a fixed point or a combinatorial obstruction.