I am a professor of
Mathematics, Statistics, and Computer Science at
the University of Illinois at Chicago.
My research concerns the geometry of low-dimensional manifolds, the deformation spaces of locally homogeneous geometric structures, and the use of analytic techniques in these areas.

Computer experiments and visualizations are an important component of my research.

- Opers and nonabelian Hodge: numerical studies (with Andrew Neitzke). Preprint, 2020. New!

Associated materials: - Asymptotics of Hitchin's metric on the Hitchin section (with Andrew Neitzke). Communications in Mathematical Physics, 2018.

doi:10.1007/s00220-018-3216-7 - Geometry of compact complex manifolds associated to generalized quasi-Fuchsian representations (with Andrew Sanders). To appear in Geometry & Topology.
- Coarse and fine geometry of the Thurston metric (with Anna Lenzhen, Kasra Rafi, and Jing Tao).
Forum of Mathematics, Sigma 8 (2020), e28.

doi:10.1017/fms.2020.3 - Holonomy limits of complex projective structures.

Advances in Mathematics 315 (2017), 427-473.

doi:10.1016/j.aim.2017.05.021 - Polynomial cubic differentials and convex polygons in the projective plane (with Michael Wolf).

Geometric and Functional Analysis 25 (2015), no. 6, 1734-1798.

doi:10.1007/s00039-015-0344-5 - Skinning maps are finite-to-one.

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

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

- Anosov representations, locally homogeneous complex manifolds, and deformation theory (with Andrew Sanders).
- Rays of conformally thick convex real projective surfaces (with Michael Wolf).
- Experiments with skinning maps (with Autumn Kent).

Some of my visualization work can be found here, but I often post these projects to my YouTube channel or Github, or to the YouTube channel of the Mathematical Computing Laboratory.

- SL(View) - Visualizing Fuchsian groups (2019)

- The PML Visualization Project (with François Guéritaud, 2012-2017)

- Fence conjecture for polygonal affine spheres (2014)

- Simple geodesics and the Birman-Series set (2011)

- Thurston's Jewel (with Jeff Brock, 2013)

- Bug on Notes of Thurston (with Jeff Brock, 2006)

- CP
^{1}structures and Bers slices (2004-2007)

- Limit sets (2001-2007)

- Ray-traced convex hulls of limit sets (2005)

- Miscellaneous images (2006-2008)

- Python for mathematical visualization: A four-dimensional case study (May 20, 2017)
- Talk at PyCon 2017 for an audience of software developers.
- Abstract
- Slides (PDF)
- See also: The PML Visualization Project

- Visualizing PML: Part 1 and Part 2 (June 30 - July 1, 2016).
- Research lecture series at the ICERM workshop Illustrating Mathematics.
- Slides for part 1 (PDF)
- Slides for part 2 (PDF)
- See also: The PML Visualization Project

- Computing the image of Thurston's skinning map (Sep 17, 2013).
- Research lecture at the ICERM workshop Exotic Geometric Structures.

- Osculation in complex projective and hyperbolic structures (Aug 10, 2012).
- Survey lecture at GEAR Retreat 2012.

- Shapes of polygons (Mar 3, 2007).
- Lecture for undergraduates at SUMS 2007.

- stokes-numerics: Compute Stokes data for polynomial opers and Higgs bundles (GitHub)
**My other recent projects on GitHub**- Older projects:
- Bear - A tool for studying Bers slices of punctured tori (at Sourceforge) (2004-2007)
- Random chords applet (2006)
- Assorted small projects (2002-2009) (from before I started using Github)

I am a co-founder and administrator of the Mathematical Computing Laboratory, an organization supporting undergraduate research in mathematics at UIC.

- UIC
- Fall 2020 - MCS 260: Introduction to Computer Science
- Spring 2019 - Math 445: Introduction to Topology I
- Spring 2019 - Math 550: Differentiable Manifolds II
- Fall 2018 - Math 320: Linear Algebra I
- Spring 2018 - Math 445: Introduction to Topology I
- Fall 2017 - Math 549: Differentiable Manifolds I
- Fall 2017 - Math 210: Calculus III (primary course content is on Blackboard)
- Spring 2017 - Math 569: Representations of surface groups
- Fall 2016 - Math 180: Calculus I
- Fall 2016 - Math 320: Linear Algebra I
- Spring 2016 - Math 535: Complex Analysis I
- Fall 2015 - Math 445: Introduction to Topology I
- Fall 2015 - Math 210: Calculus III
- 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 UIC (2008-)
- Math at Brown (2005-2008, Tamarkin Assistant Professor and NSF Postdoc)
- Math at Rice (2004-2005, NSF Postdoc)

- Math at Harvard (1999-2004, PhD student)
- Math and physics at Penn State (1995-1999, Undergraduate)

- I am a member of the National Association of Mathematicians and support their mission.

**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