Tristram Bogart
Associate Professor
Department of Mathematics
Los Andes University, Colombia
tc.bogart22 (at) uniandes.edu.co

Research

My research area is the interface between combinatorics and algebra. My primary interest is the theory of convex polytopes, both as important mathematical objects in their own right and also for their applications to toric and tropical geometry. I obtained my Ph.D. in mathematics in 2007 from the University of Washington under the direction of Rekha Thomas. Here is my CV.

Publications and Preprints

  1. An l--p switch trick to obtain a new elementary proof of a criterion for arithmetic equivalence (with Guillermo Mantilla-Soler.) To appear in Research in Number Theory.
  2. Parametric Presburger arithmetic: complexity of counting and quantifier elimination (with John Goodrick, Danny Nguyen, and Kevin Woods.) Submitted.
  3. Parametric Presburger arithmetic: logic, combinatorics, and quasi-polynomial behavior (with John Goodrick and Kevin Woods.) Discrete Analysis (2017) #4.
  4. A lower bound for the determinantal complexity of a hypersurface (with Jarod Alper and Mauricio Velasco.) Foundations of Computational Mathematics. v. 17 (3), 2017, pp. 829-836.
  5. Superlinear subset partition graphs with strong adjacency, endpoint-count, and dimension reduction (with Edward D. Kim.) Combinatorica, v. 38 (1), 2018, pp. 75--114.
  6. Finitely many smooth lattice d-polytopes with n lattice points (with C. Haase, M. Hering, B. Lorenz, B. Nill, A. Paffenholz, G. Rota, F. Santos, and H. Schenck.) Israel Journal of Mathematics v. 207 (1), 2015, pp.301-329
  7. Enumeration of Golomb Rulers and Acyclic Orientations of Mixed Graphs (with Matthias Beck and Tu Pham.) Electronic Journal of Combinatorics v. 19 (3), 2012, P42.
  8. Universal Gröbner bases of colored partition identities (with Raymond Hemmecke and Sonja Petrović.) Experimental Mathematics v. 21 (4) 2012, pp. 395-401.
  9. Hom-polytopes (with Mark Contois and Joseph Gubeladze.) Mathematische Zeitschrift v. 272, 2013, pp. 1267-1296.
  10. Obstructions to lifting tropical curves in surfaces in 3-space (with Eric Katz.) Siam Journal on Discrete Mathematics v. 26 (3), 2012 pp. 1050-1067.
  11. Riffs on the infinite ping-pong ball conundrum (with Ami Mamolo.) International Journal of Mathematical Education in Science and Technology v. 42 (5), 2011, pp. 615--623.
  12. Small Chvatal rank (with Annie Raymond and Rekha Thomas.) Mathematical Programming, Series B v. 124 (1-2), 2010, pp. 45--68.
  13. The circuit ideal of a vector configuration. (with Anders Jensen and Rekha Thomas.) Journal of Algebra v. 309 (2), 2007, pp. 518-542.
  14. Computing tropical varieties (with Anders Jensen, David Speyer, Bernd Sturmfels, and Rekha Thomas.) Journal of Symbolic Computation , v. 42, 2007, no. 1-2, pp. 54-73.


    Student Projects

    I enjoy collaboration with students and supervising theses in combinatorics and algebra.

    PhD students

    Masters Students

    Undergraduate Students


    Teaching

    Current Courses

    Past Courses



    This page was first created on 8 February 2012.
    Last update: 16 October 2018.