Class videos.
-
Lecture 01: Tue Jan 28, Course Introduction.
(
)
-
Lecture 02: Thur Jan 30, Quick review from Complex Analysis
( )
-
Lecture 03: Tue Feb 4, Introduction to extremal length and conformal modulus.
( )
-
Lecture 04: Tue Feb 6, Symmetry, Koebe's 1/4-theorem, introduction logarithmic capacity.
( )
-
Lecture 05: Tue Feb 11, Logarithmic capacity.
( )
-
Lecture 06: Thur Feb 13, Pfluger's theorem,
( )
-
Lecture 07: Tue Feb 18,
Gehring-Hayman theorem, radial limits of conformal maps
( )
-
Lecture 08: Thur Feb 20,
Finish harmonic measure, ellipse fields, geometric defiition.
( )
-
Lecture 09: Tue Feb 25,
Holder continuity of quasiconformal maps
( )
-
Lecture 10: Thur Feb 27,
Compactness of K-quasiconformal maps, locality
( )
-
Lecture 11: Tue Mar 4,
1-QC implies conformal, quasisymmetric maps
( )
-
Lecture 12: Thur Mar 6, the 3-point condition, statement of Jones-Smirnov removability theorem
( )
-
Lecture 13: Tue Mar 11,
Proof of Jones-Smirnov
( )
-
Lecture 14: Thur Mar 13,
Rickman's lemma, biLipschitz reflections
( )
-
Spring Break, no classes: March 17-21.
-
Lecture 15: Tue Mar 25,
Conformal Welding.
( )
-
Lecture 16: Thur Mar 27,
Introduction to measurable Riemann mapping theorem, absolute continuity on lines.
( )
-
Lecture 17: Tue Apr 1, QC maps are differentiable, have partial in L^2
( )
-
Lecture 18: Thur Apr 3, reverse Holder inequalities,
Borjarski's theorem, Pompeiu formula
( )
-
Lecture 19: Tue April 8, weak convergence of partials, completing proof of MRMT
( )
-
Lecture 20: Thur Apr 10, Cauchy and Beurling transform,
alternate proof of MRMT
( )
-
Lecture 21: Tue April 15, Analytic dependence on dilatation, Introduction
to Astala's area theorem
( )
-
Lecture 22: Thur Apr 17,
( )
-
Lecture 23: Tue April 22,
( )
-
Lecture 24: Thur Apr 24,
( )
-
Lecture 25: Tue Apr 29,
( )
-
Lecture 26: Thur May 1,
( )
-
Lecture 27: Tue May 6,
( )
-
Lecture 28: Thur May 8, Last class
( )