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👋 Welcome

Welcome friends to my website, my name is Tobías Martínez. I am a professor at the University of El Salvador, and I am interested in Algebraic Geometry as well as interactions between geometry and arithmetic.

Research

(Pre)Publications

  • Counting rational points on Hirzebruch-Kleinschmidt varieties over number fields
    With Sebastián Herrero and Pedro Montero. Submitted for publication. [arXiv:2407.19408]
  • Counting rational points on Hirzebruch-Kleinschmidt varieties over global function fields
    With Sebastián Herrero and Pedro Montero. Submitted for publication. [arXiv:2408.07631]
  • Mean-based iterative methods for solving nonlinear chemistry problems
    With Francisco Chicharro, Alicia Cordero, and Juan Torregrosa. Published in *Journal of Mathematical Chemistry* 58, 555–572 (2020). [DOI]

Teaching

2025

  • Precalculus
  • General Topology
  • Algebraic Topology
  • Special Program for Academic Reinforcement
  • Specialization Course for the Degree Process

2020

  • Algebra for teacher trainees
  • Ordinary Differential Equations

2019

  • General Topology
  • Abstract Algebra I
  • Algebraic Topology
  • Abstract Algebra II

2018

  • Multivariable calculus
  • Introduction to Homological Algebra
  • Abstract Algebra I
  • Introduction to Conmutative Algebra
  • Abstract Algebra II

Administrative Services

I was elected to be a member of the Asamblea General Universitaria of the UES for the 2025–2027 term.

About me

I am a Salvadoran mathematician and university lecturer with a strong background in algebraic geometry and number theory. I hold a Ph.D. in Mathematics from a joint program between the Pontificia Universidad Católica de Valparaíso, the Universidad Técnica Federico Santa María, and the Universidad de Valparaíso in Chile under the supervision of Dr. Sebastián Herrero (Universidad de Santiago de Chile) and Dr. Pedro Montero (Universidad Técnica Federico Santa María) with a doctoral internship at the University of Bath (United Kingdom).

My research interests focus on arithmetic geometry and algebraic geometry, particularly the study of rational points on algebraic varieties and the Manin conjecture as well the existence of Ulrich bundles and additive actions over algebraic varieties. I have co-authored publications in international journals and presented research at academic events in Latin America and Europe, including Chile, Colombia, Brazil, the United Kingdom and Ecuador.

Since 2014, I have been part of the Universidad de El Salvador, where I currently serve as a full-time professor in the Department of Natural Sciences and Mathematics. I have also collaborated extensively with the Programa Jóvenes Talento El Salvador, training students with high mathematical potential and mentoring projects in mathematical research and education.

Beyond research and teaching, I am committed to the academic development of my institution and the promotion of mathematics in El Salvador through conferences, seminars, and outreach programs. I have participated as a speaker in numerous national and international mathematical meetings and contributed to the organization of academic activities.

Contact

Email: tobias.martinez@ues.edu.sv

Sección de Matemática
Facultad Multidisciplinaria Oriental
Universidad de El Salvador

Km. 144 Carretera al Cuco, Cantón El Jute, San Miguel, El Salvador.