David Dumas

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

Curriculum vitæ

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.

Papers

Titles link to PDF preprints, DOI links go to published versions (often paywalled).

Opers and nonabelian Hodge: numerical studies (with Andrew Neitzke). Preprint, 2020. New!
Associated materials:
- stokes-numerics software (GitHub)
- Replication dataset for the paper
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

In Preparation

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).

Mathematical Visualization

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)
CP¹ structures and Bers slices (2004-2007)
Limit sets (2001-2007)
Ray-traced convex hulls of limit sets (2005)
Miscellaneous images (2006-2008)

Lecture videos and slides

Most of my research presentations are chalk/whiteboard talks; these are some exceptions:

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.

Lab

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

Symposium

I founded and co-organize the yearly Undergraduate Mathematics Symposium at UIC.

Abbreviated CV

Positions

Math at UIC (2008-)
Math at Brown (2005-2008, Tamarkin Assistant Professor and NSF Postdoc)
Math at Rice (2004-2005, NSF Postdoc)

Study

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

Professional memberships

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

Contact

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

Acknowledgement

This material is based upon work supported by the National Science Foundation. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.