Publications

My research interests 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 to the Informal Mathematical Proof Benchmark.

Curriculum Vitae

Education

2024–Expected 2027: 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).
2024: Short period as research assistant. P.I.: 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

March 2026: "¿Una nueva forma de hacer matemáticas?" at Coloquio de doctorandos (UCM).
February 2026: "Free Banach f-algebras" at Workshop on Free Banach Lattices (University of Wuppertal, Germany).
November 2025: "Free Banach f-algebras" at Analysis Seminar (University of Leiden, The Netherlands).
June 2025: "Free Banach f-algebras" at Seminar Banach spaces & Banach lattices (ICMAT).
June 2025: "Free Banach f-algebras" at Positivity XII (Conference Center of the TUI BLUE Manar, Tunisia).
April 2025: "Un Teorema de Kakutani (Y una trampa)" at 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: Instructor 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.
What is PlazasUni? In Spain, universities usually publish their job calls independently on their own websites or official bulletins, making them difficult for researchers to discover and track. For this reason, we created PlazasUni: an aggregator that uses traditional web scraping and AI to process the Profesor Ayudante Doctor (the spanish equivalent of tenure-track) calls of the 50 public universities in Spain.