Department of Mathematics and Philosophy

Doug LaFountain

Doug LaFountain, Professor

Specializing in Algebra, Geometry, Analysis and Topology

Education

Ph. D., University at Buffalo (Geometric Topology, William Menasco)
B.A., University at Buffalo (Mathematics, A. Dean MacGillvray)

Contact Information

Office:Morgan Hall 454
Phone: (309) 298-1529
Email: D-LaFountain@wiu.edu

Courses Taught

  • Math 102: Creative Perspectives in Mathematics
  • Math 133:Calculus with Analytic Geometry I
  • Math 211: Euclidean Geometry
  • Math 411: Geometry
  • Math 461: Introductory Topology (Independent Study)
  • Math 511: Modern Geometry (Independent Study)
  • Math 599: Differential Topology

Research Interests

Research: I am a geometric topologist who is interested in the topology and geometry of knots, links, braids and surfaces. I am particularly interested in studying these objects in contact 3-manifolds.

Research with graduate students: I am interested in working with students on any reasonable project having some connection to topics in geometric topology in either pure or applied mathematics.  For example, I have worked with graduate students on projects concerning the geometry of the curve complex (more pure math), as well as using the persistent homology of data for feature recognition (more applied math).

Research with undergraduate students: I am interested in working with students on any problem or area of research which is accessible to undergraduates and that either has a geometric/topological aspect to it, or a data science aspect to it. For the latter, I would be happy to guide students in a project in data visualization and analysis using such software as R or MATLAB.

Selected Publications

  • LaFountain, D., & W. Menasco (2017). Braid Foliations in Low-Dimensional Topology, American Mathematical Society, Graduate Studies in Mathematics 185.
  • LaFountain, D., & Penner, R. (2015). Filtered screens and augmented Teichmüller space, Geometriae Dedicata 179, 303-333.
  • LaFountain, D., & Menasco, W. (2014). Embedded annuli and Jones' conjecture, Algebraic & Geometric Topology 14, 3589-3601.
  • LaFountain, D., & Menasco, W. (2014). Climbing a Legendrian Mountain Range without Stabilization, Banach Center Publications 100, 179-196.
  • Etnyre, J., LaFountain, D., & Tosun, B. (2012). Legendrian and transverse cables of positive torus knots, Geometry & Topology 16, 1639-1689.
  • LaFountain, D. (2010). Studying uniform thickness I: Legendrian simple iterated torus knots, Algebraic & Geometric Topology 10, 891-916.