**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)__:

September 3, Qualifying Exam (room
occupied)

September 10, Dylan Thurston (Indiana University, Bloomington),

Title: From Rubber Bands to Rational Maps

Abstract: we develop parallel theories of elastic graphs and conformal
surfaces with boundary, that let us on the one hand tell
when one rubber band network is looser than another, and on the other hand tell
when one conformal surface embeds in another. As an application, we give a new
characterization of hyperbolic critically finite rational maps among branched
self-coverings of the sphere. Our characterization takes the form of a
necessary and sufficient positive criterion: a branched covering is equivalent
to a hyperbolic rational map if and only if it has a 1-dimensional object
satisfying a particular ``self-embedding'' property. Portions of this project
are joint work with Jeremy Kahn and Kevin Pilgrim.

September 17, Fred
Gardiner, On Teichmuller spaces of uniformly
asymptotic conformal circle endomorphisms and the quasidisk cocyle I.

October 1, Fred Gardiner, On Teichmuller spaces of uniformly asymptotic conformal circle
endomorphisms and the quasidisk
cocyle II.

October 8, Quanlei Fan, Explicit
eigenvalue estimates for transfer operators acting on spaces of holomorphic
functions I

October 15, Quanlei Fan, Explicit
eigenvalue estimates for transfer operators acting on spaces of holomorphic
functions II

October 22, On Teichmuller
spaces of uniformly asymptotic conformal circle endomorphisms
and the quasidisk cocyle
III.

October 29, Fred Gardiner, On Teichmuller spaces of uniformly asymptotic conformal circle
endomorphisms and the quasidisk
cocyle IV.

November 5, Fred Gardiner, On Teichmuller
spaces of uniformly asymptotic conformal circle endomorphisms
and the quasidisk cocyle V.

November 12, Fred Gardiner, On Teichmuller
spaces of uniformly asymptotic conformal circle endomorphisms
and the quasidisk cocyle
VI.

November 19, Mariela Carvacho (Chile), Title: Some invariants on the
classification of group actions

on compact Riemann surfaces.

Abstract: Given a closed orientable
topological surface

$X_g$ of genus $g \geq
2$ and $H$ an orientation

preserving self-homeomorphism of $X_{g}$

there exists (Nielsen realization) a complex

structure on $X_{g}$ such that $H$ extends

to a conformal action on $X_{g}$. It is known

that such a structure (in general) is not unique.

It depends on the number of equivalence

classes of actions of $H$ on $X_{g}$. In this
talk

the idea is to give a description of the problem

of equivalent actions and to show some recent

results about this subject.

November 26, TBA

December 3, Fred Gardiner, On Teichmuller
spaces of uniformly asymptotic conformal circle endomorphisms
and the quasidisk cocyle
VII.

December 10, Fred Gardiner, On Teichmuller
spaces of uniformly asymptotic conformal circle endomorphisms
and the quasidisk cocyle VIII.