Constructing entire functions by QC folding , Dynamics Learning Seminar, Stony Brook, March 28, 2012. I describe some of the results in the preprint of the same title. We construct entire functions with finite or bounded singular sets using quasiconformal maps of a half-plane into itself that I call ``foldings''. One applciation that I will desribe carefully is the construction of a entire function with bounded singular set that has a wandering domain. This has been open since the 1980's when Sullivan's proof for rational functions was extended to enite functions with finite singular set.
How to Draw a Conformal Map , Math Club, Stony Brook, Fall 2011, Intro to computing conformal maps using Schwarz-Christoffel formula and iterative algoithms for finding the parameters.
Conformal Maps, Optimal Meshing and Sullivan's Convex Hull Theorem , Math Dept Colloquium, Stony Brook, Thursday, March 3, 2011
Conformal Maps, Hyperbolic Geometry and Optimal Meshing , FWCG 2010, Stony Brook, Saturday, October 29, 2010
Optimal Meshing ,
Nonobtuse Triangulation of PSLGs , CG problem group, Stony Brook, Tuesday, Oct 12, 2010
Conformal Mapping in Linear Time , FWCT 2009, Tufts, Saturday, Nov 14, 2009,
Random walks in analysis , Simons Center for Geometry and Physics, Tuesday, Nov 10, 2009,
Conformal Mapping in Linear Time , CG problem session, Oct 27, 2009, Stony Brook
Counting on Coincidences , CTY Program, Oct 3, 2009, Stony Brook
An A_1 weight not comparable to any QC Jacobian , Memorial Conference for Juha Heinonen, Ann Arbor, May 12-16, 2008. 12 pages. We sketch the proof of the claim in the title. The idea is to construct a Sierpinsky carpet with the property that that certain QC images must contain a rectifiable curve. As a corollary, we show that that there is a surface in R^3 that is quasisymmetrically equivalent to the plane, but not biLipschitz equivalent.
University of Maryland, May 14, 2007 : Conformal welding and Koebe's theorem, PDF file
The following three files are talks on the same subject but with a slightly different emphasis and organization in each one. Many pages are simply figures which I explain in the talk; if you need further explaination, you can refer to my preprint of the same name, or email me.
Workshop on Computational and Conformal Geometry, Stony Brook April 20, 2007 : Conformal mapping in linear time.
UW Seattle, Wed Jan 17 2007 : An A_1 weight not comparable to any quasiconformal Jacobian
Microsoft Research, Seattle, Tue Jan 16 2007 : Conformal mapping in linear time. This file is really a superset of talk.
Wesleyan, April 6, 2006 :
Delaware.pdf : this is a pdf version of the transparences for my talk at the University of Delaware, Nov 28, 2005 ``Conformal Mapping in Linear Time''. (This is a big file, about 5M, so may take some time to download).
ABcoll.pdf : this is a pdf version of the transparences for my talk at the Ahlfors-Bers colloquium, May 21, 2005 ``Conformal Mapping in Linear Time''.
Minnesota.pdf : this is a pdf version of the transparences for my talk at Minnesota, April 14, 2005, ``Conformal Mapping in Linear Time''.
postscript : this is a postscript version of the transparences for my talk, ``A fast approximation of the Riemann map'' given at Brown University, Feb 2004.
Barrett lectures : this is a postscript version of the transparences for my June 1998 Barrett lectures talk, "Measures, martingales, manifolds and mappings". Click here for the dvi version (no figures).
postscript , pdf : this is a postscript version of the transparences for my talk ``Conformal welding and Koebe's theorem''
postscript : this is a postscript version of the transparences for my colloquium, ``Conformal maps, convex hulls and Kleinian groups''.
postscript : this is a postscript version of the transparences for my talk, ``Hausdorff dimension of limit sets''
Here is some material on Kleinian groups I perpared for my lectures in Segovia in June 1996: dvi file with definitions related to Kleinian groups. dvi file with references related to Kleinian groups. dvi file with an outline of my lectures.