Week 
Date of Thursday 
Thursday 
Friday 
Lecture notes 
Comments/Mistakes 
2 
Jan. 21 
Surfaces and curves. Intersection number. Bigon Criterion. C(S). 
Farey graph. Edge metric. Hempel's lemma. Continued fractions. 
Thursday
Friday 
Can Hempel's lemma be improved? Friday's lecture: I drew
2/3 instead of 2/3! Oops! 
3 
Jan. 28 
Train tracks. Transverse measures. Foliated tie
neighborhoods. Carrying. 
Splittings. The basic observation. Nesting
criterion. Dimension. 
Thursday
Friday 
Fixed characterization of the Farey graph. 
4 
Feb. 4 
Keane property. Dense leaves. 
No lecture due to technical difficulties. 
Thursday
 In class we gave a nonconstructive proof that pairs (track,
measure) exist having the Keane property. Give a constructive
proof. Thursday's lecture  Keane should also imply that w is
positive on every branch of τ. (Otherwise μ could contain
nonsingular boundary leaves.) 
5 
Feb. 11 
Finish dense leaves. C(S) has infinite diameter. 
Coarse geometry. 
Thursday
Friday 
Measures decompose as a finite sum of atomic measures on
curves and minimal measures. Can you use "volume growth" to prove
that the Farey graph is not quasiisometric to
H^{2} or T_{3}. 
6 
Feb. 18 
Triangles. Hyperbolicity. Combings. 
Combing implies chords. Combinatorial area. Isoperimetric
inequalities. 
Thursday
Friday 
If X is a tree then δ = 0. The converse is essentially
true (Rtrees). If (X, d) is Gromov hyperbolic then so is the
quasiisometric space (X, d/n); note that δ scales as well.
GromovHausdorff convergence. Question: are the paths in a slim
combing quasigeodesics? 
7 
Feb. 25 
Chords imply subquadratic. Subquadratic implies linear.
Linear implies stable. 
Stable implies slim. Singular flat structures. 
Thursday
Friday 
A singular flat surface. Warning: some of
the vertices have cone angle 3π/2. Thursday's lecture  The
maximum of (x + a)^2 + ((1x) + a)^2 occurs when x is as large (or
as small) as possible.

8 
Mar. 4 
Examples of halftranslation surfaces. Geodesics. Flat
annuli. 
Length. Systole map. Balance time. 
Thursday
Friday 
Squared surfaces. Singular flat metrics. (Half)translation
surfaces. Abelian/quadratic differentials. Rational billard
tables. Suspensions of interval exchange transformations... 
9 
Mar. 11 
Wide annuli. Separation lemma. Minimal spines and systole
length. 
Finish separation. Annulus inequality. Wide curves. 
Thursday
Friday 
The isoperimetic function for the plane is
x^{2}/4π. Puzzle: what is the shortest arc dividing
the equilateral triangle into two pieces of equal area?

10 
Mar. 18 
Review. Set of systoles has bounded diameter. Weighted
multicurves and their squared surfaces. W ⊂ L part
II. 
The combing. Flat length is convex. Averaging trick. Combing
triangles are slim. 
Thursday Friday 
Have a good break. 