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

- 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*. - Parametric Presburger arithmetic: complexity of counting and quantifier elimination (with John Goodrick, Danny Nguyen, and Kevin Woods.) Submitted.
- Parametric Presburger arithmetic: logic, combinatorics, and quasi-polynomial behavior (with John Goodrick and Kevin Woods.)
*Discrete Analysis*(2017) #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. - Superlinear subset partition graphs with strong adjacency, endpoint-count, and dimension reduction (with Edward D. Kim.)
*Combinatorica*, v. 38 (1), 2018, pp. 75--114. - 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 - 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. - Universal Gröbner
bases of colored partition identities (with Raymond Hemmecke and
Sonja Petrović.)
*Experimental Mathematics*v. 21 (4) 2012, pp. 395-401. - Hom-polytopes (with Mark Contois and Joseph Gubeladze.)
*Mathematische Zeitschrift*v. 272, 2013, pp. 1267-1296. - 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. - 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. - Small Chvatal rank
(with Annie Raymond and Rekha Thomas.)
*Mathematical Programming, Series B*v. 124 (1-2), 2010, pp. 45--68. - The circuit ideal
of a vector configuration. (with Anders Jensen and Rekha Thomas.)
*Journal of Algebra*v. 309 (2), 2007, pp. 518-542. - 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

- Juan Camilo Torres (current)

### Masters Students

- Juan Andr\'es Valero (Los Andes
- Tu Pham (June 2011, coadvised with Matthias Beck at San Francisco State)

### Undergraduate Students

- Julián Chitiva (December 2017)
- Daniel Tamayo (June 2017)
- Juan Camilo Azuero (June 2017)
- Juan Pablo Henao (December 2015)
- Jorge Alberto Olarte (June 2014)
- Daniel Ávila (June 2014)
- Federico Castillo (June 2012)

## Teaching

### Current Courses

- MATE 4101 [Commutative Algebra] in 2018-2
- MATE 1105 [Linear Algebra I] in 2018-2

### Past Courses

- MATE 4146 [Probabilistic Methods in Discrete Mathematics] in 2018-1
- MATE 1105 [Linear Algebra I] in 2018-1
- MATE 2510 [Honors Probability] in 2017-1
- MATE 1105 [Linear Algebra I] in 2017-1
- MATE 2113 [Enumerative and Algebraic Combinatorics] in 2016-2
- MATE 1105 [Linear Algebra I] in 2016-2
- MATE 3101 [Abstract Algebra II] in 2016-1
- MATE 1105 [Linear Algebra I] in 2016-1
- MATE 1105 [Linear Algebra I] in 2015-2
- MATE 3181/4181 [Computational Complexity] in 2015-2
- MATE 1102 [Foundations of Mathematics] in 2015-1
- MATE 2301 [Differential Equations] in 2015-1
- MATE 3172/4172 [Permutation Groups] in 2014-2
- MATE 1105 [Linear Algebra I] in 2014-2
- MATE 3113/4113 [Algebraic Combinatorics] in 2014-1
- MATE 1105 [Linear Algebra I] in 2014-1
- MATE 1103 [Number Theory] in 2013-2
- MATE 1105 [Linear Algebra I] in 2013-2
- MATE 1105 [Linear Algebra I] in 2013-1
- MATE 1102 [Foundations of Mathematics] in 2012-2
- MATE 1105 [Linear Algebra I] in 2012-2
- MATE 1214 [Integral Calculus with Differential Equations] in 2012-1
- MATE 2112 [Introduction to Combinatorics] in 2012-1
- MATE [Differential Calculus] in 2011-2
- MATH 226 [Calculus I] in autumn 2010 at San Francisco State University
- APSC 174 [Linear Algebra I] in spring 2010 at Queen's University.
- APSC 312 [Linear Algebra II] in winter 2009 at Queen's
- APSC 171 [Calculus I] in autumn 2008 at Queen's
- Math 126 [Calculus for Economics] in 2007-08 at Queen's
- Math 308 C [Linear Algebra] in spring 2007 at the University of Washington
- Math 126 E [Calculus III] in spring 2006 at Washington
- Math 120 U [Precalculus] in autumn 2004 at Washington
- Math 126 U [Calculus III] in spring 2004 at Washington
- Math 124 U [Calculus I] in summer 2003 at Washington

This page was first created on 8 February 2012.

Last update: 16 October 2018.