David Dumas

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

• Curriculum vitae (PDF)

My research concerns the geometry of low-dimensional manifolds, the deformation spaces of locally homogeneous geometric structures on such manifolds, and the of analytic techniques in these areas.

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

• My Github
• My YouTube channel

Papers

Links go to PDF preprints. The published versions may be available online if your institution or organization has a subscription to the journal.

• Asymptotics of Hitchin's metric on the Hitchin section (with Andrew Neitzke). To appear in Communications in Mathematical Physics.
• Geometry of compact complex manifolds associated to generalized quasi-Fuchsian representations (with Andrew Sanders). Submitted.
• Coarse and fine geometry of the Thurston metric (with Anna Lenzhen, Kasra Rafi, and Jing Tao). Submitted.
• 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

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

Mathematical Visualization

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:

• The PML Visualization Project (with François Guéritaud)   Updated June 2016.
  
• Fence conjecture for polygonal affine spheres
  
• Simple geodesics and the Birman-Series set
  
• Bug on Notes of Thurston (with Jeff Brock)
  
• Thurston's Jewel (with Jeff Brock)
  
• CP¹ structures and Bers slices, an overview with links to several galleries, including:
  • Bers slice images
    
  • Bers slice animations
    
  • 3D Bers slice visualization
    
• Limit sets
  
• Ray-traced convex hulls of limit sets
  
• Miscellaneous mathematical images that do not fit into the specialized galleries
  

Lecture videos

• 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.

Upcoming lectures

• May 20 - Stanford University - The Mathematical Legacy of Maryam Mirzakhani
• July 2-6 - University of Warwick - Representation varieties and geometric structures in low dimensions

Software development

• My Github hosts all recent projects
• Miscellaneous software projects (from before I started using Github)
• Bear - A tool for studying Bers slices of punctured tori (at Sourceforge) (2004-2007)
• Random chords applet (2006)

Events

Upcoming conferences and other events that I am helping to organize:

• Graduate Student Topology and Geometry Conference at UIC, April 7-8, 2018.
• Workshop on Geometry of Teichmüller Space, The Fields Institute, August 27-31, 2018
• Illustrating Mathematics, Semester program at ICERM, Fall 2019.

Lab

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

Symposium

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

Teaching

• UIC
  • 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

Miscellaneous

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.