I am an associate professor in the
Department of
Mathematics, Statistics, and Computer Science at
the University of Illinois at
Chicago.

For the Spring semester of 2015 I am a Simons Visiting Professor at the
Mathematical Sciences Research Institute, participating in the program
*Dynamics on Moduli Spaces of Geometric Structures*.

My research interests include real and complex projective structures on surfaces, Teichmüller theory, hyperbolic geometry, and Kleinian groups.

My research also incorporates computer experiments and visualizations, and I develop open-source software to help others do the same.

- Polynomial cubic differentials and convex polygons in the projective plane (with Michael Wolf). Submitted. Recently updated.
- Skinning maps are finite-to-one.

To appear in Acta Mathematica. - Holonomy limits of complex projective structures.

Submitted. - Grafting lines fellow travel Teichmüller geodesics (with Young-Eun Choi and Kasra Rafi).

International Mathematics Research Notices 2012 (2012), 2445-2492.

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

- Experiments with skinning maps (with Richard Kent).
- Complex deformations of real Anosov surface groups (with Andrew Sanders).

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

- Fence conjecture for polygonal affine spheres Recently updated.

- Visualizing PML of the five-punctured sphere

- Simple geodesics and the Birman-Series set

- Bug on Notes of Thurston (with Jeff Brock)

- Thurston's Jewel (with Jeff Brock)

- CP
^{1}structures and Bers slices, an overview with links to several galleries, including: - Limit sets

- For fun: Ray-traced convex hulls of limit sets

- Miscellaneous mathematical images that do not fit into the specialized galleries

- Osculation in complex projective and hyperbolic structures, survey lecture at GEAR Retreat 2012.
- Shapes of polygons, lecture for undergraduates at SUMS 2007.

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

- UIC
- Fall 2014 - Math 550: Differentiable Manifolds II
- Fall 2014 - Math 180: Calculus I
- Spring 2014 - MCS 481: Computational Geometry
- Spring 2014 - Math 180: Calculus I
- Spring 2013 - Math 570: Topics in Teichmüller Theory and Geometric Structures
- Spring 2013 - Math 215: Introduction to Advanced Mathematics
- Spring 2012 - MCS 481: Computational Geometry
- Fall 2011 - Math 180: Calculus I
- Spring 2011 - MCS 481: Computational Geometry
- Fall 2010 - Math 442: Differential Geometry of Curves and Surfaces
- Spring 2010 - Math 535: Complex Analysis I
- Fall 2009 - Math 180: Calculus I
- Spring 2009 - Math 442: Differential Geometry of Curves and Surfaces
- Fall 2008 - Math 210: Calculus III

- Brown
- Spring 2008 - Math 520: Linear Algebra
- Spring 2007 - Math 18: Intermediate Calculus (Multivariable)
- Spring 2006 - Math 104: Fundamental Problems of Geometry
- Fall 2005 - Math 52: Linear Algebra

- Harvard
- Fall 2002 - Freshman Seminar: Dynamics, Geometry, and Randomness
- Summer 2002 - Tutorial on Groups of Möbius Transformations
- Spring 2002 - QR26 - Decisions, Games, and Negotiation
- Summer 2001 - Tutorial on Hyperbolic Geometry

- 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.

- Zometool lets you create cool polyhedral models.

- Is your web page still readable if you remove the CSS? (The link is a bookmarklet, so you can try it on other pages.)
- I am a user of GNU/Linux (Debian and Kubuntu distributions) and an advocate of free and open source software.

**Email:**david@dumas.io-
**Office:**503 Science and Engineering Offices (SEO) -
**Full mailing address:**

Department of Mathematics, Statistics, and Computer Science

University of Illinois at Chicago

322 Science and Engineering Offices (M/C 249)

851 S. Morgan Street

Chicago, IL 60607-7045 - Public key