Publications

My research interests include: Banach spaces and Banach lattices, free objects in Functional Analysis, (positive) operator theory, ordered algebraic structures, AI for mathematics, formalization, and other computer-assisted forms of research.

(with M. A. Taylor and P. Tradacete) "Aliprantis's questions on locally solid topologies."
arXiv:2609.29498
(with J. de Dios Pont, L. Liehr, M. A. Taylor and P. Tradacete) "Banach lattices and phase retrieval: A case study for the use of AI in mathematics."
arXiv:2608.07396
"The Banach lattice Lean library."
arXiv:2608.07388
"Lattice-ordered algebras admitting a polynomial growth continuous function calculus."
arXiv:2604.20294
"Wickstead's conjecture on positive projections and non-representable Banach lattice algebras."
arXiv:2604.14697
(with P. Tradacete) "Free Banach f-algebras."
arXiv:2511.13299
"f-algebra products on AL and AM-spaces."
Math. Z. 313, 14 (2026). (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

Selected code repos

I am the maintainer of the Banach lattice Lean library.
I solved and formalized the representation problem for Banach lattice algebras.
In December 2025, I manually formalized the Kakutani–Krein theorem in Lean.
I am a contributor to the Informal Mathematical Proof Benchmark.

Notes and courses

Autoformalize your math. A guide to help mathematical researchers with no prior computer experience get started with LLM-assisted formalization.

Curriculum Vitae

Education

2024–2026: PhD in Mathematics (Universidad Autónoma de Madrid and ICMAT).
Thesis: Interactions between order and algebra in Functional Analysis: from regular operators to f-algebras.
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

2026–now: POP (Postdoctoral Orientation Programme) of my FPI-UAM contract (Universidad Autónoma de Madrid).
2024–2026: 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

2025: UAM-Santander mobility grant for young researchers.
2024: FPI-UAM fellowship for doctoral studies (UAM).
2022: JAE intro fellowship for Master's studies (ICMAT).
2022: Bachelor’s Degree Physics+Mathematics Extraordinary Award (Universitat Autònoma de Barcelona).

Invited Talks and Courses

December 2026: "TBA" at AI4Math Workshop (Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany).
November 2026: Course "Lean through Examples: From the basics to AI-assisted formalization" at RWTH Aachen University (Aachen, Germany).
September 2026: Mini-Course "Why and how to incorporate Lean to your research" at Phase Retrieval: Connecting Theory and Applications (Aachen, Germany).

Talks

September 2026: "Wickstead’s conjecture on positive projections and non-representable Banach lattice algebras." at 4th Conference on Ordered Structures and their Applications (Marseille, France).
June 2026: "Interactions between order and algebra in functional analysis" at the Analysis Seminar (UAM, Spain).
May 2026: "Wickstead's conjecture on positive projections and non-representable Banach lattice algebras" at The Kalton years 2010-2025: A workshop in homage to Nigel Kalton (IMUEx, Spain).
March 2026: "Órdenes y productos en análisis funcional" at III Encuentro de la Red de Análisis Matemático y Aplicaciones (IMAG, Spain).
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).

Research visits

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

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).

Referee activity

Positivity (x4)
Proceedings of the American Mathematical Society
Bulletin of the Korean Mathematical Society

Teaching

Fall 2026–2027: Teaching assistant Linear Algebra, Mathematics (Facultad de Ciencias, UAM).
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).

Research projects

2026–2027: Member of the research team of "Analysis and Applications of Order and Lattice Structures" (CSIC, COOPB25033).
2025–2029: Member of the research team of "Banach lattices, Geometric Valuation Theory and Machine Learning" (Ministerio de Ciencia, Innovación y Universidades, PID2024-162214NB-I00).

Training courses

2025: "Competencias digitales para la investigación: herramientas digitales para la gestión de proyectos y para la gestión de la información" (2 ECTS).
2025: "Competencias digitales para la investigación: comunicación de ideas de manera efectiva con recursos digitales interactivos" (2 ECTS).

Other

2024–Now: Instructor at Pequeño Instituto de Matemáticas: challenging problem sessions for high school students.
November 2024: Imparted 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.
I use Arch, btw.