Class videos.
passcode Kesten<2/3
- Lecture 01: Course Overview, Part I. Jan 27, 2022 ( )
- Lecture 02: Course Overview, Part II. Feb 1, 2022 ( )
- Lecture 03: Modulus and Extremal Length Feb 3, 2022 ( )
- Lecture 04: Symmetry and Koebe's theorem Feb 5, 2022 ( )
- Lecture 05: Hyperbolic metric and uniformization theorem Feb 10, 2022 ( )
- Lecture 06: The Gehring-Hayman theorem Feb 15, 2022 ( )
- Lecture 07: Boundary behavior of conformal maps Feb 17, 2022 ( )
- Lecture 08: Logarithmic capacity Feb 22, 2022 ( )
- Lecture 09: Equilbrium measures, Pfluger's theorem Feb 24, 2022 ( )
- Lecture 10: Harmonic measure, Ahlfors Distortion, Beurling's estimate March 1, 2022 ( )
- Lecture 11: Kesten's theorem March 3, 2020 ( )
- Lecture 12: Levy's construction of Brownian motion March 8, 2022 ( )
- Lecture 13: Brownian motion is nowhere differentiable March 10, 2022 ( )
- Lecture 14: Dimension of the Brownian graph and trace March 22, 2022 ( )
- Lecture 15: The Markov property, maximum of Brownian motion, Wald's lemma March 24, 2022 ( )
- Lecture 16: Area of Brownian motion, the Law of the Iterated Logarithm March 29, 2022 ( )
- Lecture 17: The Stong Law of Large numbers, the Dirichlet problem March 31, 2022 ( )
- Lecture 18: Guest lecture by Amanda Turner on random growth April 5, 2022 ( )
- Lecture 19: Conformal invariance of Brownian paths in 2 dimensions April 7, 2022 ( )
- Lecture 20: Introduction to dyadic martigales April 12, 2022 ( )
- Lecture 21: Convergence and divergence of dyadic martingales, Bloch harmonic functions April 14, 2020 ( )
- Lecture 22: Makarov's theorem: harmonic measure has dimension at most 1 April 19, 2022 ( )
- Lecture 23: Makarov's theorem: harmonic measure has dimension at least 1, Makarov's LIL April 21, 2022 ( )
- Lecture 24: Makarov's LIL for harmonic measure is sharp April 26, 2022 ( )
- Lecture 25: Extending Markarov's theorem from quasidisks to general Jordan domains April 28, 2022 ( )
- Lecture 26: The F. and M. Riesz theorem, rectifiable boundaries May 3, 2022 ( )
- Lecture 27: McMillian's twist point theorem, mutual signualarity of harmonic measure on fractals May 5, 2022 ( )