About Me
I was born in Madrid where I studied both maths and physics, though I have also enjoyed the universities and daily life of some other awesome places like Vienna, Brussels, Barcelona, Montréal, or Rio de Janeiro. I did my Ph.D. thesis in mathematical physics under the supervision of Eduardo J.S. Villaseñor (UC3M) and Fernando Barbero (IEM-CSIC).
Short CV
- Assistant Professor (UdeM, 2025-)
- Assistant Professor (UC3M, 2023-2025)
- AARMS postdoctoral scholar with Ivan Booth and Hari Kunduri (MUN, 2021-2023)
- NSF postdoctoral scholar with Abhay Ashtekar (IGC-PSU, 2019-2021)
- ICREA postdoctoral fellowship with Eva Miranda (GEOMVAP-UPC, 2019)
- ERC postdoctoral fellowship with Daniel Peralta (ICMAT, 2018)
- Ph.D. in mathematical physics with a La Caixa Fellowship (UC3M and IEM-CSIC, 2014-2018)
- Research stay with Hanno Sahlmann (Institute for Quantum Gravity - Erlangen, 2017)
- Research stay with Martin Bauer (TU Wien, 2016)
- Master in Fundamental Mathematics (UCM, 2011-2012)
- Degree in Mathematics with the Second National Prize of Spain (UCM, 2006-2011)
- 1 year Degree in Mathematics (SICUE at UB, 2009-2010)
- Degree in Physics (UCM, 2008-2013)
- 1 year Master in Physics (Erasmus at ULB, 2012-2013)
Contact Information
UdeM
- Mathematics and Statistics
Pabellón André-Aisenstadt, UdeM.
Office: 4441 - juan.margalef umontreal.ca
RESEARCH
Interests
My research interests lie in the mathematical foundations of General Relativity and classical field theories, with particular emphasis on the role of boundaries. The geometric nature of the underlying spaces frequently brings forward subtle and technically delicate issues in functional analysis, differential geometry, and symplectic geometry. The overarching goal of this work is to gain a deeper understanding of how a consistent theory of quantum gravity might behave.
I am currently focusing on the geometric formulation of the Covariant Phase Space approach and its application to a variety of field theories. In parallel, I am interested in the computational aspects of these methods, which has led me to develop the xCPS package within the xAct bundle.
ACADEMIC ACTIVITIES
List of conferences and seminars
Conferences and seminars I have organized
OUTREACH
Interests
The importance of science communication is already well acknowledged as a way to connect with society, explain our research, and generate vocation in young students. That is why I am so passionate about it! I love engaging people with topics that might seem difficult or tedious at first. Showing them examples where maths and physics appear in their everyday life. Making them wonder about fundamental questions that can be taken for granted.
TEACHING
Teaching statement
As an educator, I am committed to sharing my passion for mathematics and physics with my students. My goal is to spark their interest and help them appreciate the beauty of these subjects. I want to engage them in the subject to make it easier for them to learn. To achieve this, I draw upon my experience in science communication and always try to connect abstract concepts to real-world examples.
Courses
Université de Montréal
- Calculus I (MAT1400) — Winter 2026, Fall 2025
Universidad Carlos III de Madrid
- Advanced Mathematics (Aerospace Engineering) — 2023, 2024
- Linear Algebra — Sound Eng. (2024), Computer Science (2015, 2017)
- Calculus I — Industrial Eng., Electrical Eng., Computer Science (2016, 2017)
Memorial University of Newfoundland
- Vector Calculus (MATH-3202) — Spring 2023
- Differential Geometry (MATH-4230) — Winter 2023
- Diff. Manifolds & Riemannian Geometry (MATH-6230) — Winter 2023
Penn State University
- General Relativity (PHYS-510) — 2019
Mini-courses
- At the Boundary of Covariant Phase Space: New Insights into Field Theories — XVII International ICMAT Summer School on GMC (2025)
Mini-couse on the Covariant Phase Space of field theories. Topics included: differential geometry, symplectic geometry, differential topology, bicomplex formalism, infinite-jet bundle formalism and its applications to field theories. - Introduction to the Covariant Phase Space — Memorial University of Newfoundland (2020)
Mini-couse on the Covariant Phase Space of field theories. Topics included: differential geometry, symplectic geometry, differential topology, bicomplex formalism, infinite-jet bundle formalism and its applications to field theories. -
Vector Bundles — Universitat Politècnica de Catalunya (2019)
Part of the Differential Geometry course taught by Eva Miranda. Topics included vector bundles and subbundles, bundle maps, integration, and cohomology. -
Geometrization of Field Theories — Universitat Politècnica de Catalunya (2019)
Mini-course at the 1st Research Introduction Symposium of the UPC. Introduction to manifolds, vector bundles, semi-Riemannian and symplectic geometry, followed by Newtonian, Lagrangian, and Hamiltonian mechanics. -
An Invitation to b-Symplectic Geometry: From Quantization to Periodic Orbits — ICMAT (2019)
Mini-course at the 13th International ICMAT Summer School on Geometry, Mechanics, and Control. Covered b-manifolds, b-tangent bundles, b-cohomology, and applications to geometry and dynamics.