I am a professor of
Mathematics, Statistics, and Computer Science at
the University of Illinois at Chicago.

My primary research areas are differential geometry, geometric topology, and complex analysis. Most of my research projects focus on moduli spaces of locally homogeneous geometric structures on manifolds, often in cases where complex-analytic techniques can be applied.

I use computer experiments in my research, and I pursue mathematical visualization projects for both research and expository purposes.

- Opers and nonabelian Hodge: numerical studies (with Andrew Neitzke).

Experimental Mathematics (2021).

doi:10.1080/10586458.2021.1988006Associated materials:

- Uniformization of compact complex manifolds by Anosov homomorphisms (with Andrew Sanders).

Geometric and Functional Analysis 31 (2021), no. 4, 815-854.

doi:10.1007/s00039-021-00572-6 - Geometry of compact complex manifolds associated to generalized quasi-Fuchsian representations (with Andrew Sanders).

Geometry & Topology 24 (2020), no. 4, 1615-1693.

doi:10.2140/gt.2020.24.1615 - 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 - Asymptotics of Hitchin's metric on the Hitchin section (with Andrew Neitzke).

Communications in Mathematical Physics 367 (2019), 127-150.

doi:10.1007/s00220-018-3216-7 - 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 rays 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 - Complex projective structures. (Survey)

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.

J. Diff. Geom. 74 (2006), 93-118.

Journal link: article / erratum

- Visualizing Complex Anosov Families (2023)

- 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 (with Andrew Neitzke)
- Replication dataset for the paper "Opers and nonabelian Hodge: numerical studies" (with Andrew Neitzke)
**My other recent projects on GitHub**- Older projects (unmaintained):

- UIC
- Spring 2024 - MCS 275: Programming Tools and File Management
- Fall 2023 - Math 547: Algebraic Topology I
- Spring 2023 - MCS 275: Programming Tools and File Management
- Fall 2022 - Math 549: Differentiable Manifolds I
- Spring 2022 - MCS 275: Programming Tools and File Management
- Fall 2021 - MCS 260: Introduction to Computer Science
- Spring 2021 - MCS 275: Programming Tools and File Management
- 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 in 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)

- Member of National Association of Mathematicians.

- I use
**he/him**pronouns. (Why pronouns?) **Email is the best way to reach me:**david@dumas.io · ddumas@uic.edu-
**Office:**722 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