"Le savant n'étudie pas la nature parce que cela est utile; il l'étudie parce qu'il y prend plaisir et il y prend plaisir parce qu'elle est belle. Si la nature n'était pas belle, elle ne vaudrait pas la peine d'être connue, la vie ne vaudrait pas la peine d'être vécue. Je ne parle pas ici, bien entendu, de cette beauté qui frappe les sens, de la beauté des qualités et des apparences; non que j'en fasse fi, loin de là, mais elle n'a rien à faire avec la science; je veux parler de cette beauté plus intime qui vient de l'ordre harmonieux des parties, et qu'une intelligence pure peut saisir."
Henri Poincaré

My research lies on Algebraic Combinatorics, Computational Mathematics, Optimization, Topological Graph Theory and Statistics.

Published papers

  1. The Degree-Distance and Transmission-Adjacency Matrices (with O. Zapata), conditionally acepted in Computational and Applied Mathematics, 2024. [https://arxiv.org/abs/2212.05297]
  2. Covering and 2-degree-packing numbers in graphs (with C. Rubio-Montiel, A. Vázquez-Avila), in Open Journal of Discrete Applied Mathematics, 2024. [https://arxiv.org/abs/1707.02254]
  3. Computing sandpile configurations using integer linear programming (with M.C. Vargas and C.E. Valencia), in Chaos, Solitons and Fractals, 2023. [https://arxiv.org/abs/2008.13672]
  4. Codeterminantal graphs (with A. Abiad, K. Heysse, M.C. Vargas), in Linear Algebra and its Applications, 2022. [https://arxiv.org/abs/1910.12502]
  5. The assignment problem revisited (with S.L. Perez, C.E. Valencia, M.C. Vargas), in Optimization Letters, 2022. [https://arxiv.org/abs/1810.03562]
  6. Extremal Mathematicians, in Journal of Humanistic Mathematics, 2022. Igor Pak does a deeper reflection on this topic in his blog
  7. The characterization of graphs whose sandpile group has fixed number of generators (with M.D. Barrus, J. Sinkovic, R.R. Villagrán), in Trends in Mathematics, 2021. To be presented at EUROCOMB'21
  8. Enumeration of cospectral and coinvariant graphs (with A. Abiad), in Applied Mathematics and Computation, 2021. [https://arxiv.org/abs/2008.05786]
  9. Graphs with few trivial characteristic ideals (with M.D. Barrus, J. Sinkovic, R.R. Villagrán), in Linear Algebra and its Applications, 2021. [https://arxiv.org/abs/2004.00172]
  10. The structure of sandpile groups of outerplanar graphs (with R.R. Villagrán), in Applied Mathematics and Computation, 2021. [https://arxiv.org/abs/2005.01314]
  11. On a problem of Henning and Yeo about the transversal number of uniform linear systems whose 2-packing number is fixed (with A. Vazquez-Avila), in Discrete Mathematics Letters, 2020. [https://arxiv.org/abs/1710.02501]
  12. On graphs with 2 trivial distance ideals, in Linear Algebra and its Applications, 2020. [https://arxiv.org/abs/1807.07992]
  13. Distance ideals of graphs (with L. Taylor), in Linear Algebra and its Applications, 2020. [https://arxiv.org/abs/1709.10178]
  14. Critical ideals and applications, in Matemática Contemporânea, 2019. Presented in VIII Latin American Workshop on Cliques in Graphs, August 9-11, 2018.
  15. On transversal and 2-packing numbers in uniform linear systems (with G. Araujo-Pardo, C. Rubio-Montiel, A. Vázquez-Avila), in AKCE International Journal of Graphs and Combinatorics, 2019. [https://arxiv.org/abs/1903.08984]
  16. Critical ideals, minimum rank and zero forcing number (with J. C.-H. Lin), in Applied Mathematics and Computation, 2019. [http://arxiv.org/abs/1710.03386]
  17. On two-quotient strong starters for F_q (with C. Rubio-Montiel and A. Vázquez-Ávila), in Utilitas Mathematica, 2019. [https://arxiv.org/abs/1609.05496]
  18. Outperforming Several Heuristics for the Multidimensional Assignment Problem (with S.L. Peréz, C.E. Valencia, M.C. Vargas and F.J. Zaragoza), in Proceedings of the 15th International Conference on Electrical Engineering, Computing Science and Automatic Control 2018.
  19. Graphs with real algebraic co-rank at most two, in Linear Algebra and its Applications, 2018. [https://arxiv.org/abs/1711.00374]
  20. Small clique number graphs with three trivial critical ideals (with C.E. Valencia), in Special Matrices, 2018. [https://arxiv.org/abs/1311.5927]
  21. The crossing number of the cone of a graph (with A. Arroyo, M. Derňár and B. Mohar), in SIAM Journal of Discrete Mathematics 2018. [https://arxiv.org/abs/1608.07680]
  22. Digraphs with at most one trivial critical ideal (with C.E. Valencia & A. Vazquez-Avila), in Linear and Multilinear Algebra, 2018. [https://arxiv.org/abs/1703.08621]
  23. Critcal ideals of digraphs (with C.E. Valencia and A. Vazquez-Avila), in Matemática Contemporânea, 2017. Presented in VII Latin American Workshop on Cliques in Graphs, November 8-11 2016.
  24. Critical ideals of graphs with twin vertices (with H.H. Corrales & Carlos E. Valencia), in Advances in Applied Mathematics, 2017. [http://arxiv.org/abs/1504.06257]
  25. The crossing number of the cone of a graph (with A. Arroyo, M. Derňár and B. Mohar), in Lecture Notes in Computer Science vol. 9801, 2016. Presented in Graph Drawing'16 by Bojan Mohar (slides).
  26. Graphs with few trivial critical ideals (with C.E. Valencia), in Electronic Notes in Discrete Mathematics, 2015. Presented in LAGOS'15.
  27. Graphs with two trivial critical ideals (with C.E. Valencia), in Discrete Applied Mathematics, 2014. [http://arxiv.org/abs/1304.4211]
  28. Dimension Reduction in Principal Component Analysis for Trees (with B. Aydin, E. Bullitt, A. Ladha, and C.E. Valencia), in Computational Statistics & Data Analysis, 2014. [http://arxiv.org/abs/1202.2371]
  29. On the sandpile group of the cone of a graph (with C.E. Valencia) in Linear Algebra and its Applications, 2012. [http://arxiv.org/abs/1004.3321]

Chapter

  1. Sandpiles (with C. Merino) in Sriraman, B. (eds) Handbook of Visual, Experimental and Computational Mathematics, Springer, Cham, 2023.

Student

  1. Ralihe R. Villagrán Ph.D. from CINVESTAV-IPN 2021 (co-directed with Carlos E. Valencia). Currently, he is postdoc at Worcester Polytechnic Institute.

Patent

  1. Selection of data paths. US Patent Application. Ref. 83037389. (with B. Aydin, K. Guler, C. E. Valencia) Hewlett-Packard Company, 2012.

Copyright

  1. Knotj3d. INDAUTOR Reg. 03-2007-100314141100-01 (with O. Gutú and R. Lopéz-Hérnandez) 2007.

Teaching

  1. Algebraic graph theory at Universidad Nacional Autónoma de México
  2. Mathematical economics at Universidad La Salle México

My academic profiles

Google scholar
MathSciNet
Math genealogy
zbMATH Open
Orcid
Scopus
Web of Science

CV

CV (EN)
CV (SP)

Thesis

Ph.D. - Critical ideals of a graph and dimension reduction in tree space
M.Sc. - The sandpile group of a multigraph
B.Sc. - Knot theory and its applications
Ernesto Lupercio: ¿Cómo trabajaba Lefschtez?
Alberto Verjovsky: Lefschetz dormía bastante: por su edad, ya tomaba su siesta. Luego se levantaba, tomaba una pluma con sus brazos especiales, y se sentaba a escribir. Lo veía mirando a través de sus anteojos, y escribía, y escribía bastante; se ve que pensaba mucho, soñaba mucho y, justo es confesarlo, dormía mucho en las conferencias. En todas las conferencias a las que asistí en las que estaba él, se durmió. Lo asombroso era que, cuando se despertaba, hacía la mejor pregunta: su subconsciente o no sé qué. Siempre iba al centro. Sus preguntas siempre eran como un dardo al corazón de la pregunta. Veía la esencia. Como todo gran matemático, iba exactamente al meollo del problema y, a partir de eso discutía. Nunca lo vi en el diván. Ya ves lo que decía Alan Connes sobre la importancia del diván —de leer, de tener tiempo de ocio, leisure time, para pensar— para un matemático y que, a veces, es difícil convencer a la esposa de que estás trabajando. El diván simboliza el leisure time: el "ocio activo". Por ejemplo, actividades como estar en algunas redes sociales no califican porque te quitan libertad, te distraen haciendo otras cosas en lugar de usar tu tiempo para reflexionar. Necesitas tiempo de ocio positivo. Lo que quiere decir con eso es que, además de todo lo demás, un matemático necesita tiempo de libertad y, por lo tanto, una universidad, una institución académica debe contar con eso: darle tiempo de ocio al investigador para pensar y desarrollar ideas; después, las clases.

Entrevista completa en el enlace.