**Extremal**** Length Geometry Seminar**

Organized by Fred Gardiner (frederick.gardiner@gmail.com) with Yunping Jiang and Linda Keen

Department of Mathematics

CUNY Graduate Center

Fall of 2014 Schedule

Wednesday, 3:30pm-4:55pm (__Math
Thesis Room, Rm. 4214-03)__:

January 28, Fred Gardiner, Kobayashi's and Carath\'eodory's metrics on Teichmuller
space I

February 4, Fred Gardiner,
Kobayashi's and Carath\'eodory's
metrics on Teichmuller space II

February 11, Monday
Schedule, Fred Gardiner, Kobayashi's and Carath\'eodory's metrics on Teichmuller
space III

February 18, Fred
Gardiner, Kobayashi's and Carath\'eodory's
metrics on Teichmuller space IV

February 25, Fred
Gardiner, Kobayashi's and Carath\'eodory's
metrics on Teichmuller space V

March 4, Jeremy Kahn, On a compactification of Teichmuller space I

March 11, Jeremy Kahn, On a compactification of Teichmuller space II

March 18, Irwin Kra, Maskit coordinates: metrics
and geodesic discs I

March 25, Linda Keen, on Schottky groups I

April 1, Linda Keen, on Schottky groups II

April 8, Spring Recess

April 15, TBA

April 22, Moira Chas, Computer driven
theorem and questions in geometry I

Consider an orientable surface $S$ with negative
Euler characteristic,

a minimal set of generators of the fundamental
group of $S$, and

a constant curvature $-1$ metric on $S$.
Each unbased homotopy class
$C$

of closed oriented curves on $S$ determines three numbers:
the word length

(that is, the minimal number of letters needed
to express $C$ as a cyclic word

in the generators and their inverses), the
minimal geometric self-intersection number,

and finally the geometric length. These three
numbers can be explicitly computed

(or approximated) using a computer. We
will discuss relations between these numbers

and their statistical structure as length
becomes large.

April 29, Moira Chas, Computer driven
theorem and questions in geometry II

Consider
an orientable surface $S$ with negative Euler
characteristic,

a minimal set of generators of the fundamental
group of $S$, and

a constant curvature $-1$ metric on $S$. Each
unbased homotopy class $C$

of closed oriented curves on $S$ determines
three numbers: the word length

(that is, the minimal number of letters needed
to express $C$ as a cyclic word

in the generators and their inverses), the
minimal geometric self-intersection number,

and finally the geometric length. These three
numbers can be explicitly computed

(or approximated) using a computer. We will discuss
relations between these numbers

and their statistical structure as length
becomes large.

May 6, Irwin Kra, Maskit coordinates: metrics
and geodesic discs II

May 13, Fred Gardiner, The Tower of Hanoi
puzzle as an expanding Thurston map.