## Lecture recording links

Thursday, August 27, 2020 , Passcode 035&FsC. (include the .),
overview of the course

Tuesday, Sept 1, 2020 , Passcode: T$pnWSN9, overview continued

Class on Thursday Sep 3 canceled

Tuesday, Sept 8, 2020 , Passcode: $MB3ix5R, overview continue,
hyperbolic conditions

Class on Thursday Sept 10 canceled (internet problem)

Tuesday, Sept 15, 2020 , Passcode: Ug6jc%k% , introduction to
geometric function theory, Dirichlet class, Schwarzians, quasiconformal maps

Thursday, Sept 17, 2020 , Passcode: Kb8%U3Dm
conformal welding, comparision to results for little, Bloch class, BMO,
Sobolev spaces,

Tuesday, Sept 22, 2020 , Passcode: 7alWk7&v
Mobius energy, Jones conjecture

Thursday, Sept 24, 2020 , Passcode: 307Rvg+P
multi-resolution families, excess length

Tuesday, Sept 29, 2020 , Passcode: UjxTb37%
beta-numbers, quasiconformal and biLipschitz reflections in plane

Thursday, Oct 1, 2020 ,
Passcode: .49JKcjb
Menger curvature, start biLipschitz involutions

Tuesday, Oct 6, 2020 ,
Passcode: K5xY^^D%
BiLipschitz involutions implies beta-number estimate

Thursday, Oct 8, 2020 ,
Access Passcode: UC@fmS1E Beta-numbers and epsilon-numbers are
equivalent, Introduction to traveling salesman theorem

Tuesday, Oct 13, 2020 ,
Access Passcode: J0S#7sF0
Starting proof of TST, splitting convex sets, diameters decrease with splitting.

Thursday, Oct 15, 2020 ,
Access Passcode: g@RUg1kq
Prove convex covering sets are well distributed, Finish proof of upper bound for curves
and general sets

Tuesday, Oct 20 , 2020 , Access Passcode: 6VlD1#z?
Guest speakers Martin Chuaqui (Schwarzian derivatives) and Yilin Wang
(Loewner energy).

Thursday, Oct 22, 2020 , Access Passcode: m8!3t8d$
Start proof of lower bound in TST; integral geometry, good pairs lemma

Tuesday, Oct 27, 2020 , Access Passcode: N96+wC1e
Finish proof of lower bound for diameter in TST;
large betas.

Thursday, Oct 29, 2020 , Access Passcode: EjfZ5g$T
Proof of lower bound in TST for chord-length;
crossing lemma, chains of boxes with
large betas.

Tuesday, Nov 3, 2020 , Access Passcode: vi==j7y5
Guest lecture by Dragomir Saric: universal Teichmuller space,
Farey tesselation of hyperbolic disk (see notes posted on webpage)

Thursday, Nov 5, 2020 , Access Passcode: E8Qw&wxQ
Hyperbolic geometry, convex hulls, delta-numbers.

Tuesday, Nov 10, 2020 , Access Passcode: 4Xus+Gx^
WP curves are boundaries of surfaces with square integrable
principle curvatures, C. Epstein's theorem on the Gauss map

Thursday, Nov 12, 2020, Part 1 , Access Passcode: 21r.x%z%
Thursday, Nov 12, 2020, Part 2 , Access Passcode: !3aWyn1x
Due to a technical glitch (images were fuzzy for some participants)
I had to restart the meeting after about 10 minutes. Thus the
lecture was recorded into two pieces (one short, one long).
Topics covered:
BiLipschitz involutions, Seppi's estimate, minimal surfaces
with total finite curvature, renormalized area.

Tuesday, Nov 17, 2020 , Access Passcode: t1!ZW7WG
Isoperimetric inequalities on negatively curved surfaces.

Thursday, Nov 19, 2020 , Access Passcode: fd?W.0dB
Dyadic cylinders (last new material from preprint)

Tuesday, Dec 1, 2020 , Access Passcode: qYr!st4a
Guest lectures by David Mumford and Rafe Mazzeo. Due to a mistake on my part,
the first 5 minutes of Mumford's talk was not recorded (sorry).
David lost his connection about 20 minutes into this recording, so Rafe
began his remarks, and David finished his presentation after Rafe finished
his. Despite a few technical problems, this was a very informative and
useful session.

Mumford's slides

Thursday, Dec 3 2020 , Access Passcode:
ir7bh3?j
Last class: discussion of some open problems.

Thanks to everyone who attended the class this semester. It was a great experience
for me (though a bit exhausting). I hope it was worth the time you devoted to it.
Please give me your feedback on what worked and what didn't, and let me know
of any research that develops out of this..