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 Fang, Explicit eigenvalue estimates for transfer operators acting on spaces of holomorphic functions I

 

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

 

October 22, Fred Gardiner, 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, Eric Schippers (University of Manitoba)

                       Title: Some applications of conformal field theory to Teichmuller theory

                       Abstract: Consider the collection of compact Riemann surfaces of genus g with n punctures, endowed with n non-overlapping   

                                       Conformal maps of the disk into neighbourhoods of each puncture. The moduli space of these "rigged" surfaces, up to

                                       conformal equivalence, was considered by Friedan-Shenker and Vafa.  It plays a central role in conformal field 

                                       theory.  David Radnell and I showed that this moduli space can be identified (up to a discrete group action) with the

                                       quasiconformal Teichmuller space of surfaces of genus g with n boundary curves. In this talk I will describe some

                                       applications of this correspondence to Teichmuller theory.  Namely, it can be used to prove that the quasiconformal

                                       Teichmuller space of bordered surfaces fibers over the Teichmuller space of compact surfaces. 

                                       This in turn can be used to construct a Teichmuller space of surfaces of genus g with n boundary curves,

                                       modelled on L^2 Beltrami differentials.  This Teichmuller space is in some sense the largest space

                                       on which the Weil- Petersson metric converges.  Joint work with D. Radnell and W. Staubach.

 

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

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, Yunping Jiang, Infinmum of metric entropy for Anosov diffeomorphisms

                        and expanding circle endomorphisms preserving Lebegue measure.

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

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

 

 

Spring of 2014 Schedule

Fall of 2013 Schedule