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

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).

To appear in Geometric and Functional Analysis. - Skinning maps are finite-to-one.

Acta Mathematica 215 (2015), no. 1, 55-126.

doi:10.1007/s11511-015-0129-6 - 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).

I also have a YouTube channel.

The links in this list go to gallery pages, most of which contain some explanation of the mathematical background:

- Fence conjecture for polygonal affine spheres

- The PML Visualization Project (with François Guéritaud) Updated June 2016.

- 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 2015 - Math 445: Introduction to Topology I
- Fall 2015 - Math 210: Calculus III (my section is managed through Blackboard)
- 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 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