Class videos.
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Mon Jan 26 Class canceled, university closed because of snow.
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Lecture 01: Wed Jan 28
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)
Introduction to course:
Random walks, Brownian motion, harmonic measure,
Riemann mapping theorem, true trees.
Due to technical problems and a fire alarm class lasted only 50 minutes,
so I will finish the introduction in next class.
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Lecture 02: Mon Feb 2
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Chapter 1, Section 1:
harmonic measure on half-plane and disk
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Lecture 03: Wed Feb 4
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Chapter 1, Section 2: Fatou's theorem on non-tangential limits.
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Mon Feb 9 Class canceled.
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Lecture 04: Wed Feb 11
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Chapter 1, Sections 3 and 4: Caratheodory's theorem and Koebe's 1/4 therorem.
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Lecture 05: Mon Feb 16
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Chapter I, Sections 4 and 5: hyperbolic metric and the Hayman-Wu theorem.
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Lecture 06: Wed Feb 18
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Chapter II, Sections 1 and 2: Schwarz alternating method, Green's function.
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Lecture 07: Mon Feb 23
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University was closed today for a snowstorm, but I recorded a lecture on Chapter II, Sections 3 and
4 to be viewed later by the students. This material is only summarized quickly with no proofs and is not
needed for most of what follows in the course.
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Lecture 08: Wed Feb 25
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Chapter III, Section 1: Capacity and Greens function
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Lecture 09: Mon Mar 2
( )
Chapter III, Sections 3 and 4: Energy intergral and
equilibrium distribution
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Lecture 10: Mon Mar 9
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Chapter III, Sections 5, 6, 7: Wiener's solution
of Dirichlet problem, regular points, Wiener's series.
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Lecture 11: Wed Mar 11
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Chapter III, Sections 8 and 9: Polar sets, sets of harmonic measure zero,
and estimates for harmonic measure.
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Mon Feb 16 and Wed March 18 No class, Spring Break.
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Lecture 12: Mon March 22
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Chapter IV, Sections 1-3 and Chapter V, Section 1:
I was away this day, so
lecture was pre-recorded.
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Lecture 13: Wed March 25
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Chapter IV, Sections 5 and 6 and Chapter V, Section 1
Extremal distance, harmonic measure estimates,
and Denjoy conjecture.
I was away this day, so
lecture was pre-recorded.
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Lecture 14: Mon March 30
( )
Chapter V, Section 3: Reduced extremal distance.
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Lecture 15: Wed April 1
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Appendex A (Hardy spaces) and Chapter VI, Section 1
(the F. and M. Riesz Theorem).
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Lecture 16: Mon April 6
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Chapter VI, Sections 2 and 3: Privalov's and
Plessner's theorems and accessible points
(pre-recorded lecture).
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Lecture 17: Wed April 8
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Chapter VI, Section 4: McMillian's cone point theorem
(pre-recorded lecture).
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Lecture 18: Mon April 13
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Chapter VI, Section 5: Makarov's upper bound.
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Lecture 19: Wed April 15
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Chapter VI, Section 6: Pommerenke's extension: harmonic measure lives
on sigma-finite length.
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Lecture 20: Mon April 20
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Chapter VII, Sections 1 and 2: Bloch functions and conformal maps.
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Lecture 21: Wed April 22
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Chapter VII, Section 3: Quasicircles.
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Lecture 22: Mon April 27
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Chapter VIII, Section 1: Law of the Iterated Logarithm for Bloch functions.
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Lecture 23: Wed April 29
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Chapter VII, Section 2: harmonic measure and Hausdorff dimension
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Lecture 24: Mon May 4
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Complete Section VIII.2, proof of McMillan's twist point theorem
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Lecture 25: Wed May 6
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Last Class. DLA (Diffusion Limited Aggregation).