Short Bio
Since 2014, I am researcher at BANXICO (the Central Bank of Mexico), where my principal activities consist in developing and implementing optimization models. Between 2011 and 2012, I visited the HP Labs at Palo Alto, CA to work with Burcu Aydin, Kemal Guler, Lyle Ramshaw, Pano Santos and Bob Tarjan. There, we developed algorithms to study tree-structure data, and supported the development of assignment algorithms for resource planning allocation.I received my Ph.D. degree in 2014 from the Department of Mathematics at CINVESTAV under supervision of Carlos E. Valencia. Since then, I started my research on Algebraic Combinatorics and Discrete Applied Mathematics. In particular, I focus on algebraic invariants of graphs such as Laplacian matrices, sandpile groups and critical ideals.
Extended CV
Journal Papers
Algebraic combinatorics
Small clique number graphs with three trivial critical ideals (with C. E. Valencia) submitted.Digraphs with at most one trivial critical ideal (with Carlos E. Valencia & Adrián Vázquez-Ávila) accepted in Linear and Multilinear Algebra.On two-quotient strong starters for F_q (with Christian Rubio-Montiel and Adrián Vázquez-Ávila) accepted in Utilitas Mathematica.
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].
Graphs with two trivial critical ideals (with C. E. Valencia), in Discrete Applied Mathematics, 2014. [http://arxiv.org/abs/1304.4211]
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]
Operations ResearchOptimizing the production cost of minting with mixed integer programming (with J. Aguilera, C. Guadarrama, R. Martinez-Noriega & A. Sanchez-Flores) submitted.
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]
Graph theoryThe crossing number of the cone of a graph (with Alan Arroyo, Marek Derňár and Bojan Mohar) submitted.
Covering and 2-packing numbers in graphs (with Christian Rubio-Montiel and Adrián Vázquez-Ávila) submitted.
Conference papers
Graphs with few trivial critical ideals (with Carlos E. Valencia), in Electronic Notes in Discrete Mathematics, 2015. Presented in LAGOS'15.
The crossing number of the cone of a graph (with Alan Arroyo, Marek Derňár and Bojan Mohar), in Lecture Notes in Computer Science vol. 9801, 2016. Presented in Graph Drawing'16 by Bojan Mohar (slides).
Ciritcal ideals of digraphs (with Carlos E. Valencia and Adrián Vázquez-Ávila) accepted in Matemática Contemporânea. Presented in VII Latin American Workshop on Cliques in Graphs, November 8-11 2016.
Patent
Selection of data paths. US Patent Application. Ref. 83037389. (with B. Aydin, K. Guler, C. E. Valencia) Hewlett-Packard Company, 2012.
Copyright
Knotj3d. INDAUTOR Reg. 03-2007-100314141100-01 (with O. Gutú and R. Lopéz-Hérnandez) 2007.
Undergraduate and PhD thesis
Code
JGraphs - (github) A code in Java that serves as a graphical interface for computing the critical group and the critical ideals of a digraph. It requires Sage and Emacs. But if wanted, the code can be modified to use an alternative Computer Algebra System (a previous version used Mathematica and Macaulay2) or Text Editor. This also can be used to export in Tikz format the rectilinear drawing of the graph.
CSandPile - (github) CSandPile is a tool developed in C++ for computing the group operations of the recurrent representatives of non-negative configurations of a graph. It helps to understand the combinatorial structure of the group operations of the recurrent configurations that generate the sandpile group of a graph.
RiceRocks - (github) (It doesn't work on Internet Explorer) Just push play. Enjoy and modify! I coded a version for Android watch it here.
CSandPile - (github) CSandPile is a tool developed in C++ for computing the group operations of the recurrent representatives of non-negative configurations of a graph. It helps to understand the combinatorial structure of the group operations of the recurrent configurations that generate the sandpile group of a graph.
RiceRocks - (github) (It doesn't work on Internet Explorer) Just push play. Enjoy and modify! I coded a version for Android watch it here.
KnotJ3D - (github) This is a Java applet, which draws 3D tangles. There are implemmented some operations like sum and closure. It was coded in Java3D, so you need to install it to run it.
Recent presentations
Academic profiles
Recent workshops
VII Latin American Workshop on Cliques in Graphs, November 8-11 2016
Interesting readings
Mathematics and Programming in the Cloud with CoCalc
IFORS Developing Countries On-Line Resources page "Operational Research" (OR) is the discipline of applying advanced analytical methods to help make better decisions. By using techniques such as problem structuring methods and mathematical modelling to analyze complex situations, Operational Research gives executives the power to make more effective decisions and build more productive systems.
Euler's Gem "... Euler worked on coinage for the national mint..."
Las dos culturas de las matemáticas by W.T. Gowers
The Misfortunes of a Trio of Mathematicians Using Computer Algebra Systems. Can We Trust in Them? by Antonio J. Durán, Mario Pérez, and Juan L. Varona
How to build an economic model in your spare time by Hal R. Varian
"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
"The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas, like the colors or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics."
G.H. Hardy
Chris Carter
