Publications

My research topics include: Banach spaces and Banach lattices, free objects in Functional Analysis, (positive) operator theory, and ordered algebraic structures.

(with P. Tradacete) "Free Banach f-algebras."
arXiv:2511.13299
"f-algebra products on AL and AM-spaces."
arXiv:2507.08435
(with P. Tradacete) Banach lattice AM-algebras.
Proceedings of the American Mathematical Society 153.06 (2025): 2565-2577. (arXiv:2409.18500)
Band projections and order idempotents in Banach lattice algebras.
Journal of Mathematical Analysis and Applications 543.2 (2025): 129045. (arXiv:2407.09149)
(with P. Tradacete) Band projections in spaces of regular operators.
Transactions of the American Mathematical Society 377.07 (2024): 5197-5218. (arXiv:2310.08318)
(with J. Calsamiglia, J. Bergou and E. Bagan) "Phase estimation with limited coherence."
arXiv:2207.05656

Lean and AI

I have formalized the Kakutani–Krein theorem in Lean (GitHub repo).
I am a contributor of the Informal Mathematical Proof Benchmark.

Curriculum Vitae

Education

2024–now: PhD in Mathematics (Universidad Autónoma de Madrid and ICMAT).
Advisor: Pedro Tradacete Pérez.
2022–2023: Master in Mathematics and Applications (Universidad Autónoma de Madrid).
Master thesis: Band projections on the space of regular operators over a Banach lattice.
Supervisor: Pedro Tradacete Pérez.
2017–2022: Bachelor Degree in Mathematics (Universitat Autònoma de Barcelona).
Bachelor thesis: The classification of finitely generated modules over a PID and its application to canonical form theory.
Supervisor: Francesc Perera Domènech.
2017–2022: Bachelor Degree in Physics (Universitat Autònoma de Barcelona).
Bachelor thesis: Quantum phase estimation with limited coherence.
Supervisor: Emili Bagan Capella.

Positions

2024–now: Contratado predoctoral FPI-UAM (Universidad Autónoma de Madrid).
February 2024: Research assistant of José Manuel Conde Alonso (Universidad Autónoma de Madrid).

Awards and fellowships

2024: FPI-UAM fellowship for doctoral studies (UAM).
2022: JAE intro fellowship for Master's studies (ICMAT).
2022: Bachelor’s Degree Extraordinary Award (Universitat Autònoma de Barcelona).

Research visits

Sep. 2025–Dec. 2025 (3 months): University of Leiden. Host: Marcel de Jeu.

Talks

February 2026: "Free Banach f-algebras" (University of Wuppertal, Germany).
November 2025: "Free Banach f-algebras" (University of Leiden, The Netherlands).
June 2025: "Free Banach f-algebras" Seminar Banach spaces & Banach lattices (ICMAT).
June 2025: "Free Banach f-algebras" Positivity XII (Conference Center of the TUI BLUE Manar, Tunisia).
April 2025: "Un Teorema de Kakutani (Y una trampa)" Coloquio Junior (UAM).
March 2025: AM-algebras at Structures in Banach Spaces (Erwin Schrödinger Institute, Austria).
May 2024: "Inner band projections on Banach lattice algebras" at Focus Week Lattice structures in Analysis and Applications (ICMAT).
April 2024: "Inner band projections on Banach lattice algebras" at Seminar Lattice structures in Analysis and Applications (ICMAT).
July 2022: "On the covering dimension of Cu-semigroups and Cu-morphisms" at Barcelona Introduction to Mathematical Research (BGSMath, CRM, University of Barcelona, Spain).
March 2022: "Cómo hacer cosas a pedazos (en espacios de Banach)" at XVII Encuentro de la Red de Análisis Funcional y Aplicaciones (Universidad de La Laguna, Spain).

Organization of conferences

2024–2026: Seminar on Banach spaces & Banach lattices (ICMAT)
April 2024–June 2024: Research term Lattice Structures in Analysis and Applications (ICMAT).

Teaching experience

Spring 2025–2026: Teaching assistant Mathematics II, Chemical Engineering (Facultad de Ciencias, UAM).
Spring 2024–2025: Teaching assistant Algebra II, Physics (Facultad de Ciencias, UAM).
Spring 2024–2025: Teaching assistant Calculus II, Data Engineering (Escuela Politécnica Superior, UAM).

Other

2024–Now: Teacher at Pequeño Instituto de Matemáticas: challenging problem sessions for high school students.
November 2024: Workshop for high school students at "XXIV Semana de la Ciencia y de la Innovación de Madrid".
2021: Internship at Sangaku Maths.

Random facts

I designed and programmed this website from scratch: it consists of ~280 lines of HTML and ~160 lines of CSS.