Carlos A. Alfaro


Carlos Alejandro Alfaro Montúfar

Banco de México

alfaromontufar [at] gmail [dot] com

carlos [dot] alfaro [at] banxico [dot] org [dot] mx 

Research Interests

I have an ample experience dealing with economical and technological problems, ranging from implementing optimization models for the Mexican central bank to creating video games for Android, as well as, simulating 3D RNA recombination. Mathematically, my research lie on algebraic and topological combinatorics, as well as statistics and optimization.

"It should be obvious that a solution in the industry must go further than a linear regression or a greedy algorithm."

Short Bio

I am researcher at BANXICO (the central bank of Mexico) since 2014, where my principal activities consist in designing and implementing optimization models as well as analyzing data. I received my Ph.D. degree in 2014 from the Department of Mathematics at CINVESTAV under supervision of Carlos E. ValenciaBetween 2011 and 2012, I visited the HP Labs at Palo Alto, CA to work with Burcu AydinKemal GulerLyle RamshawPano Santos and Bob Tarjan. There, I developed algorithms to study tree-structure data, and supported the implementation of assignment algorithms for resource planning allocation. Currently, I belong to the Mexican research system (level I).

Extended CV


Journal Papers

Algebraic combinatorics

  1. On graphs with 2 trivial distance ideals submitted.
  2. Distance ideals of graphs (with L. Taylor) submitted.
  3. Critical ideals, minimum rank and zero forcing number (with Jephian C.-H. Lin) in Applied Mathematics and Computation, 2019 [].
  4. Graphs with real algebraic co-rank at most two in Linear Algebra and its Applications, 2018. []
  5. Small clique number graphs with three trivial critical ideals (with C. E. Valencia) in Special Matrices, 2018. [].
  6. On two-quotient strong starters for F_q (with Christian Rubio-Montiel and Adrián Vázquez-Ávila) accepted in Utilitas Mathematica [].
  7. Digraphs with at most one trivial critical ideal (with Carlos E. Valencia & Adrián Vázquez-Ávila) in Linear and Multilinear Algebra, 2018. []
  8. Critical ideals of graphs with twin vertices (with H. H. Corrales & Carlos E. Valencia) in Advances in Applied Mathematics, 2017 [].
  9. Graphs with two trivial critical ideals (with C. E. Valencia), in Discrete Applied Mathematics, 2014. []
  10. On the sandpile group of the cone of a graph (with C. E. Valencia), in Linear Algebra and its Applications, 2012. []

Operations Research

  1. 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. []
  2. The equivalence between two classic algorithms for the assignment problem (with S.L. Peréz, C.E. Valencia and M.C. Vargas) submitted.
  3. Computing sandpile configurations using integer linear programming (with C.E. Valencia and M.C. Vargas) submitted.

Graph theory

  1. The crossing number of the cone of a graph (with Alan Arroyo, Marek Derňár and Bojan Mohar) in SIAM Journal of Discrete Mathematics 2018.[].
  2. Covering and 2-packing numbers in graphs (with Christian Rubio-Montiel and Adrián Vázquez-Ávila) submitted.

Linear systems

  1. On transversal and 2-packing numbers in uniform linear systems (with G. Araujo-Pardo, C. Rubio-Montiel, A. Vázquez-Avila) accepted in AKCE International Journal of Graphs and Combinatorics. []
  2. On a problem of Henning and Yeo about the transversal number of uniform linear systems whose 2-packing number is fixed (with A. Vázquez-Ávila) submitted.

Conference papers

  1. Graphs with few trivial critical ideals (with Carlos E. Valencia), in Electronic Notes in Discrete Mathematics, 2015. Presented in LAGOS'15.
  2. 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).
  3. Critcal ideals of digraphs (with Carlos E. Valencia and Adrián Vázquez-Ávila) in Matemática Contemporânea. Presented  in VII Latin American Workshop on Cliques in Graphs, November 8-11 2016.
  4. Outperforming Several Heuristics for the Multidimensional Assignment Problem (with S.L. Peréz, C.E. Valencia, M.C. Vargas and F.J. Zaragoza), in IEEE. Presented in 2018 15th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE).

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


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


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.

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

Critical ideals and applications, presented in LAAW 2018
Critical ideals and applications, presented in LAWCG 2018
Aplicaciones de los ideales criticos, presented in seminario de matemáticas at UASLP

Academic profiles

My math-genealogy 
My citations
My MathSciNet profile

Recent workshops

Scaling limits of dynamical processes on Random graphs, May 19-24, 2019

VIII Latin American Workshop on Cliques in Graphs, August 9-11, 2018

Linear Algebra and its Applications Workshop, July, 30-31, 2018

Graduate Research Workshop in Combinatorics, May 21 - June 1, 2018

Beyond Planarity: Crossing Numbers of Graphs, June 11-17 2017

Interesting readings

The books that inspiring me more are:

 - The mathematics of chip-firing by Caroline J. Klivans

 - The Sharing Economy by Arun Sundararajan
 - In Pursuit of the Traveling Salesman by William J. Cook
 - The Master Algorithm by Pedro Domingos
 - The Poincare Conjecture: In Search of the Shape of the Universe by Donal O’Shea

 - The Granularity of Growth by Patrick Viguerie, Sven Smit and Mehrdad Baghai

 - Review of "Algorithms for data science" by Richard and Nicholas De Veaux (An interesting overview of data science)

"When it was announced... that I was going to become CEO... I asked the top 150 people in the company to meet with me for an hour each -150 hours in total. And I gave each of them the same five questions, which they received in advance: What three things do you want to change? What three things do you want to keep? What are you most worried I might do? What do you want me to do? Is there anything else you want to talk about? And I just listened for an hour. Many of the people came in with stuff written down, and in the case of those who didn't, I took notes. And then I tabulated all responses, coming up with a pretty accurate and timely picture of what the top 150 leaders in the company wanted to do. I put all of this together and sent a memo to the entire company summarizing my findings. These interviews gave me the mandate to do what I needed to do. It created a shared reality for the company and allowed people to begin aligning around a number of goals."

More interesting readings:

- Guillermo del ¡Torito, no te mueras! by Gabriel Rodriguez (La ciencia en México también es un arte, y tampoco es fácil)

Pamela Harris: The Mathematical Rise and Social Contribution of a Dreamer by Ricardo Cortez and Federico Ardila 

- Ph.D.'s, come out of the closet! by Lina Nilsson
- "Euler worked on coinage for the national mint" cited from Euler's Gem
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

Some links

        Mathematics and Programming in the Cloud with CoCalc

         Nature of Code

Recent MX$20 coins
50 years of integer programming 1958-2008

        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.

Hispanic Heritage: Pano Santos, a Beautiful Mind (watch an inspiring interview from FOX NEWS to Pano Santos, a scientist of HP Labs)