Teaching

Instructor

2025 – 2026

Geometry of Varieties, MS in Modeling, Mathematical Research, Statistics and Computing, University of Zaragoza, Spring 2026.

Linear Geometry, BS in Mathematics, University of Zaragoza, Fall 2025.

2024 – 2025

Geometry of Varieties, MS in Modeling, Mathematical Research, Statistics and Computing, University of Zaragoza, Sprint 2025.

Disciplinary Content of Mathematics, MS in Teacher for Mandatory Secondary Education, Baccalaureate, Vocational Training and Language, Arts and Sports Education, University of Zaragoza, Sprint 2025.

General Topology, BS in Mathematics, University of Zaragoza, Fall 2024.

2023 – 2024

Geometry of Varieties, MS in Modeling, Mathematical Research, Statistics and Computing, University of Zaragoza, Spring 2024.

Mathematics 2, BS in Informatics Engineering, University of Zaragoza, Fall 2023.

2021 – 2023

Mathematics, BS in Optics and Optometry, University of Zaragoza, Fall 2021, 2022, Spring 2022, 2023.

Geometry of Varieties, MS in Modeling, Mathematical Research, Statistics and Computing, University of Zaragoza, Spring 2022, 2023.

Linear Geometry, BS in Mathematics, University of Zaragoza, Fall 2021, 2022.

2016 – 2021

Statistics, BS in Industrial Organization Engineering, CUD Zaragoza, Fall 2018, 2019, 2020.

Differential Equations, BS in Industrial Organization Engineering, CUD Zaragoza, Fall 2016, 2017.

Cryptography: congruences, Fermat’s little theorem, and RSA, Advanced Cyber Defense Course, Academy of Engineers at Hoyo de Manzanares (Madrid), February 2016, 2017, 2018, 2019.

Assistant

2010 – 2016

Differential Equations, BS in Industrial Organization Engineering, CUD Zaragoza, Fall 2014, 2015.

Calculus, BS in Industrial Organization Engineering, CUD Zaragoza, Fall 2011, 2012, 2013.

Linear Algebra, BS in Industrial Organization Engineering, CUD Zaragoza, Spring 2011.

Introduction to algebra and cryptography, Basics of digital information processing and protection, Centre de recherche des écoles de Saint-Cyr (France), September 2015, 2016, 2017, 2018, 2020.

Course grader and assistant

2009 – 2010

Algebraic Topology, BS in Mathematics, Lab works, University of Zaragoza, Fall 2009.

Linear Geometry, BS in Mathematics, Exercises and lab works, University of Zaragoza, Fall 2009.

2008 – 2009

Introduction to Algebra, BS in Mathematics, Exercises and lab works, Univ. Zaragoza, Spring 2009.

Algebraic Geometry, BS in Mathematics, Lab works, University of Zaragoza, Spring 2009.

Linear Geometry, BS in Mathematics, Exercises and lab works, University of Zaragoza, Fall 2008.

Riemannian Geometry, BS in Mathematics, Exercises, University of Zaragoza, Fall 2008.

2007 – 2008

Introduction to Algebra, BS in Mathematics, Exercises and lab works, Univ. Zaragoza, Spring 2008.

Algebraic Geometry, BS in Mathematics, Exercises, University of Zaragoza, Spring 2008.

Teaching assistant

2004 – 2005

Galois Theory, BS in Mathematics, Exercises, University of Seville, Spring 2005.

Linear Algebra, BS in Statistics, Exercises, University of Seville, Spring 2005.

Textbook

Álgebra Lineal y Aplicaciones (with M.V. Sebastián-Guerrero and R. Villacampa-Guitiérrez). Textos Docentes, 7, pp. 1–312, Centro Universitario de la Defensa, 2012.

Mentoring

Module of logarithmic derivations and topology of plane curves. PhD thesis of Wayne Ng Kwing King at the University of Zaragoza and University of Pau and Pays de l'Adour with Jean Vallès, Present.
Effective computation of the minimal model for APL algebras. PhD thesis of Carlos Alquézar Baeta at the University of Zaragoza with M.A. Marco-Buzunariz, Present.
Free divisors and hyperplane arrangements. Undergraduate research supervisor for Sixto Martínez at the Univesity of Zaragoza with E. Artal, June 2025.
Effective computation of the Sullivan model of a topological space and its rational homotopy type. Master thesis supervisor for Carlos Alfonso Alquézar Baeta at the University of Zaragoza with M.A. Marco-Buzunariz, September 2024.
Lenstra's elliptic curve factorization method. Undergraduate research supervisor for Miguel Clavo at the University of Zaragoza with A. Lozano, September 2023.
Gröbner bases and their applications to multivariable cryptographic systems. Undergraduate research supervisor for Borja Royo-Blázquez at the University of Zaragoza, July 2022.
Gröbner bases and applications to resolution of sudokus. Undergraduate research supervisor for Bárbara Zapater-Zarroca at the University of Zaragoza with J.I. Cogolludo, February 2021.
Multivariate cryptography, Gröbner bases, and attacks. Undergraduate research supervisor for Emilio Casanova-Biscarri at the University of Zaragoza with J.I. Cogolludo, July 2019.
Algebraic number theory and Fermat's last theorem. Master thesis supervisor for Nicolas Ridet at Centre de recherche des écoles de Saint-Cyr Coëtquidan (CREC) with Guy Chassé, January 2017.
Gröbner bases and applications to cryptography. Undergraduate research supervisor for Almudena Agudo-Carnicer at the University of Zaragoza with J.I. Cogolludo, July 2017.
The use of elliptic curves in cryptography. Master thesis supervisor for Matthieu Bonnefont at Centre de recherche des écoles de Saint-Cyr Coëtquidan (CREC) with Guy Chassé, January 2016.
Identificación de sustancias explosivas mediante la parametrización/caracterización de curvas planas. Undergraduate research supervisor for Alejandro Gracia-Benito at the University of Zaragoza with L. Rández and J. Martínez, July 2015.
Game theory and military decition making. Undergraduate research supervisor for Andrés Zamora-Beamud at Centro Universitario de Zaragoza (CUD) with José-Antonio Fernández-Alfaro, June 2015.