Areas of interest

  • Commutative Algebra (Research Area)
  • Algebraic Geometry
  • Combinatorics and computational Algebra

Recent Papers

  1. Indicator functions, v-numbers and Gorenstein rings in the theory of projective Reed--Muller-type codes, (with M. González-Sarabia, H. Muñoz-George, J. A. Ordaz and E. Sáenz-de-Cabezón), Des. Codes Cryptogr., to appear.
  2. Normally torsion-free edge ideals of weighted oriented graphs, with G. Grisalde and J. Martínez-Bernal), Comm. Algebra 52 (2024), no. 4, 1672-1685.
  3. A duality theorem for the ic-resurgence of edge ideals, European J. Combin. 109 (2023), paper no. 103656, 18 pp.
  4. Normality criteria for monomial ideals, (with L. A. Dupont, H. Muñoz-George), Results Math. 78 (2023), no. 1, paper no. 34, 31 pp.

Monomial Algebras

Click here for the web page for the Second Edition of my book Monomial Algebras. This book brings together several areas of pure and applied mathematics, and shows how monomial algebras are related to polyhedral geometry, combinatorial optimization, and combinatorics of hypergraphs.

Interests and Current Activities

I am currently an Associate Editor of Journal of Algebraic Combinatorics and Bulletin Mathematique, and was a member of the boards of Communications in Algebra, Boletin de la Sociedad Matematica Mexicana and Aportaciones Matematicas.



Here are some of my favorite destinations on the Web. Check them out and if you know some other great places please let me know!


Department of Mathematics
Av. IPN 2508, Col. San Pedro Zacatenco,
Ciudad de México. C.P. 07360.
Office 044
☏ Office Phone: (+52) 55 5747 3870
✉ E-mail: vila [at] math.cinvestav.mx