Publications

14. 14. (w/ R. Davidson) Combinatorial and Computational investigations of Neighbot-Joining bias. [Submitted] Article | arXiv | Suplementary Material
    
    

14. 13. (w/ F. Sottile, and R. Williams) Classification of Schubert Galois groups in Gr(4,9). [Submitted] Article | arXiv | Suplementary Material
    
    

12. 12. (w/ A. Leykin, F. Sottile, R. Vakil, and J. Verschelde) Numerical Schubert calculus via the Littlewood-Richardson homotopy algorithm. [Accepted] Article | arXiv | Macaulay2 code
    
    

11. 11. (w/ S. Cepeda and C. Uhler) Exact goodness-of-fit testing for the Ising model. Scandinavian Journal of Statistics, Vol. 44, no. 2 (2017), pp. 285--306. Article | arXiv.
    
    

10. 10.(w/ J. Rodriguez) Critical points via monodromy and local methods. Journal of Symbolic Computation SI: Numerical Algebraic Geometry. Vol. 79, part 3 (2017), pp. 559-574. Article | arXiv | Macaulay2 code
    
    

9. 9. (w/ F. Sottile) Experimentation in the Schubert Calculus. Schubert Calculus - Osaka 2012, Advanced Studies in Pure Mathematics, Vol. 71 (2016), pp. 295-336. Article | arXiv
   
   

8. 8. (w/ N. Hein, C. Hillar, F. Sottile and Z. Teitler ) The monotone secant conjecture in the real Schubert calculus. Experimental Mathematics, 24:3 (2015), pp. 261-269.  Article | arXiv | (Extended Abstract MEGA 2011  PDF | Slides).
   
   

7. 7. (w/ C. Brooks and F. Sottile) Galois groups of Schubert problems of lines are at least alternating. Transactions of the American Mathematical Society, 367 (2015), no. 6, pp. 4183-4206. Article | arXiv
   

6. 6. (w/ D. Haws, A. Takemura and R. Yoshida) Markov degree of the three-state toric homogeneous Markov chain model. Beiträge zur Alg. und Geom., March 2014, Vol. 55, no. 1, pp. 161-188. Article | arXiv
   
   

5. 5. (w/ C. Hillar ) Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals. Journal of Symbolic Computation, Vol. 50, March 2013, pp. 314-334. Article | arXiv | Macaulay2 code | Errata
   
   

4. 4. (w/ C. Brooks and F. Sottile) An inequality of Kostka numbers and Galois groups of Schubert problems. DMTCS Proc. 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), pp. 981-992. Article | arXiv
   
   

3. 3. (w/ L. García-Puente, N. Hein, C. Hillar, J. Ruffo, F. Sottile and Z. Teitler ) The Secant Conjecture in the Real Schubert Calculus.  Experimental Mathematics, 21:3 (2012), pp. 252-265. Article | arXiv
   
   

2. 2. (w/ D. Haws and R. Yoshida) Degree bounds for a minimal Markov basis for the three-state toric homogenous Markov chain model. Harmony of Gröbner bases and Modern Industrial Society. 2012. pp. 63-98. Article | arXiv
   
   

1. 1.(w/ C. Hillar, L. García-Puente, J. Ruffo, Z. Teitler, S. Johnson and F. Sottile ) Experimentation at the Frontiers of Reality in Schubert Calculus. Gems in Experimental Mathematics, Contemporary Mathematics, vol. 517, Amer. Math. Soc., Providence, RI, 2010, pp. 365-380. Article | arXiv
   
   

Selected Talks and Lectures

1. • "Modelos Estadísticos Algebraicos y sus bases de Markov" - Taller de Matemáticas discretas, Topología, Álgebra, Probabilidad y Computación, Univ. del Papaloapan. 7-10 September 2016.
   

2. • "Galois groups of Schubert problems" - Colloquium Math. Department, Univ. of Innsbruck. April, 2014.
   

3. • "Goodness-of-fit testing in Ising models" - Colloquium Stats. Department, Univ. of Kentucky. August, 2013.
   

4. • "The Monotone Secant conjecture in the real Schubert calculus" - MEGA 2011, Stockholm Univ. May, 2011.
   

Theses

1. • Galois groups of Schubert Problems. Ph.D. Thesis directed by Frank Sottile, Texas A&M University.
   
   

2. •Optimization of the Buchberger Algorithm by Planar Resolutions. (in Spanish) Master Thesis directed by Javier Elizondo Huerta, Instituto de Matemáticas, UNAM.
   
   

3. • Riemann-Roch Theorem. (in Spanish) Undergraduate Thesis directed by Javier Elizondo Huerta, UNAM.