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.

 

 

Spring of 2014 Schedule