The following are several research topics that I am interested in:
The explicit resolution of Fermat-type equations.
Determination of explicit bounds for the solutions of Diophantine equations.
Computational number theory, including the efficient computation of modular forms and points on abelian varieties.
Application of number theory techniques to other areas, like coding theory.
The following is a list of my most relevant mathematical writings. Any comments and feedback are greatly appreciated!
All papers are available on my arxiv page and, if there is associated code, in my GitHub.
On generalised Pythagorean triples over number fields, to appear in the Rivista Matematica della Università di Parma (preprint available in arxiv).
On the conductor of a family of Frey hyperelliptic curves, joint with Lucas Villagra Torcomian, available in arxiv (MAGMA code available here).
Perfect codes over non-prime power alphabets: an approach based on Diophantine equations, Mathematics 2024, 12(11), 1642, available online here (preprint available in arxiv and MAGMA code available here).
Asymptotic Fermat's Last Theorem for a family of equations of signature (2, 2n, n), Mathematika 2024, 70 (4), available online here (preprint available in arxiv and MAGMA code available here).
On differences of perfect powers and prime powers, submitted, available in arxiv (MAGMA code available here).
Applications of the modular method to Diophantine equations, PhD Thesis at the University of Manchester, supervised by Dr. Gareth Jones and Dr. Martin Orr, available here.
Arithmetic geometry in curves of genus larger than one, dissertation in the MSc of Mathematics and Foundations of Computer Science at the University of Oxford, supervised by Prof. Victor Flynn, available here.
Dominios de Dedekind (in Spanish), dissertation in the Double BSc in Mathematics and Computer Science at the Universidad Autónoma de Madrid, supervised by Dr. Ana Bravo-Zarza, available here.