David Dumas

Articles

• Holonomy limits of complex projective structures. Updated version (October 2011).
  Submitted.
• Grafting lines fellow travel Teichmüller geodesics (with Young-Eun Choi and Kasra Rafi).
  International Mathematics Research Notices 2011.
  doi:10.1093/imrn/rnr104
• Bers slices are Zariski dense (with Richard Kent).
  Journal of Topology 2 (2009), no. 2, 373-379.
  doi:10.1112/jtopol/jtp014
• Survey: Complex projective structures.
  In Handbook of Teichmüller Theory, Volume II. Ed. Athanase Papadopoulos. EMS, 2009.
  doi:10.4171/055
• Slicing, skinning, and grafting (with Richard Kent).
  American Journal of Mathematics 131 (2009), no. 5, 1419-1429.
  doi:10.1353/ajm.0.0072
• Projective structures, grafting, and measured laminations (with Michael Wolf).
  Geometry & Topology 12 (2008), no. 1, 351-386.
  doi:10.2140/gt.2008.12.351
• Distribution of intersection lengths of a random geodesic with a geodesic lamination (with Martin Bridgeman).
  Ergodic Theory and Dynamical Systems 27 (2007), no. 4, 1055-1072.
  doi:10.1017/S0143385706001040.

  [ Related: Random chords java applet ]

• The Schwarzian derivative and measured laminations on Riemann surfaces.
  Duke Mathematical Journal 140 (2007), no. 2, 203-243.
  doi:10.1215/S0012-7094-07-14021-3.
• Grafting, pruning, and the antipodal Map on Measured Laminations.
  The PDF linked here is an updated version of the paper published in J. Diff. Geom. 74 (2006), 93-118. It includes the correction that is the subject of this erratum.
  Journal link: article / erratum

In Preparation

• Skinning maps are finite-to-one.

  Using analytic and algebraic geometry in the character variety, we show that Thurston's skinning map of Teichmüller space has finite fibers. Along the way, we introduce a natural stratified Kähler structure on the space of measured laminations.

Mathematical Images

Links go to gallery pages, most of which contain some explanation of the mathematical background:

• Simple geodesics and the Birman-Series set  New.
  
• Bug on Notes of Thurston (with Jeff Brock)
  
• CP¹ structures and Bers slices, an overview with links to several galleries, including:
  • Bers slice images
    
  • Bers slice animations
    
  • 3D Bers slice visualization
    
• Limit sets
  
• For fun: Ray-traced convex hulls of limit sets
  
• Miscellaneous mathematical images that do not fit into the specialized galleries
  

Slides from past talks

Note: These are old lectures. I now prefer to use chalkboards for my presentations.

• Slicing, Skinning, and Grafting (PDF)
  
  • Geometry and Dynamics in Surfaces and 3-Manifolds, Brown University (5/3/2007)
  • Complex geometry seminar, Johns Hopkins University (4/26/2007)
• Grafting Coordinates for Teichmüller Space (PDF)
  
  • AMS sectional meeting at the University of Connecticut (10/29/2006)
• Analysis and Geometry of CP¹ Structures on Surfaces (PDF)
  
  • Teichmüller Space, Classical and Quantum workshop at MFO (6/2/2006)
  • 2006 Georgia Topology Conference (5/20/2006)
  • Teichmüller Theory and Moduli Problems workshop at HRI (1/10/2006)

Collaborators

• Martin Bridgeman (Boston College)
• Young-Eun Choi
• Richard Kent (Brown University)
• Kasra Rafi (Univeristy of Chicago)
• Michael Wolf (Rice University)

Places

• Math at Brown, where I was a Tamarkin Assistant Professor and NSF Postdoc for three years (2005-2008).
• Math at Rice, where I spent the 2004-2005 academic year as an NSF Postdoc.
• Math at Harvard, where I spent five years as a graduate student.
• Math and physics at Penn State, where I spent four years as an undergraduate.
• Pennsbury School District, where I was a student for nine years.

Things

• Zometool lets you create cool polyhedral models.

Computing

• Is your web page still readable if you remove the CSS? (The link is a bookmarklet, so you can try it on other pages.)
• This page is hosted and maintained without the use of Microsoft software.
• I am a user and supporter of Debian GNU/Linux, and an advocate of free and open source software.