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