Class videos.
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Lecture 01: Course Overview, Part I.
August 27, 2020 (
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Lecture 02: Course Overview, Part II.
September 1, 2020 ( )
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Lecture 03: Course Overview, Part III.
September 8, 2020 ( )
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Lecture 04: Dirichlet class, Schwarzians and QC maps.
September 15, 2020 ( )
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Lecture 05: Conformal welding and Sobolev spaces.
September 17, 2020 ( )
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Lecture 06: Mobius energy and the Jones conjecture.
September 22, 2020 ( )
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Lecture 07: Multi-resolution families and excess length.
September 24, 2020 ( )
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Lecture 08: Beta-numbers and QC involutions in the plane.
September 29, 2020 ( )
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Lecture 09: Menger curvature and biLipschitz involutions.
October 1, 2020 ( )
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Lecture 10: Good biLipschitz involutions implies beta-number estimate.
October 6, 2020 ( )
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Lecture 11: Beta-numbers and epsilon-numbers are equivalent.
October 8, 2020 ( )
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Lecture 12: Proof of TST, Part I (splitting convex sets).
October 13, 2020 ( )
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Lecture 13: Proof of TST Part II (split sets are well distributed).
October 15, 2020 ( )
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Lecture 14: Guest speakers Martin Chuaqui (Schwarzian derivatives) and Yilin Wang (Loewner energy).
October 20 , 2020 ( )
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Lecture 15: Proof of TST, Part III (integral geometry).
October 22 , 2020 ( )
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Lecture 16: Proof of TST, part IV (the lower bound).
October 27, 2020 ( )
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Lecture 17: Proof of TST party V (finish proof).
October 29, 2020 ( )
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Lecture 18: Guest speaker Dragomir Saric (universal Teichmuller space and the Farey tesselation).
November 3, 2020 ( )
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Lecture 19: Hyperbolic convex hull and delta-numbers.
November 5, 2020 ( )
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Lecture 20: Finite total curvature and the Gauss map.
November 10, 2020 ( )
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Lecture 21: Seppi's estimate for minimal surfaces.
November 12, 2020 ( )
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Lecture 22: Isoperimetric inequalities and renormalized area.
November 17, 2020 ( )
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Lecture 23: Dyadic cylinders.
November 19, 2020 ( )
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Lecture 24: Guest Speakers David Mumford and Rafe Mazzeo.
December 1, 2020 ( )
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Lecture 25: Open questions and future directions.
December 3, 2020 ( )