M. de León, R. Izquierdo-López, M. Lainz, "The Spencer cohomology and integrability of multisymplectic structures".
arXiv: arXiv:2607.05267
Research
The main topic of my PhD is multisymplectic geometry, the natural finite-dimensional geometric framework for the study of classical field theories, along with related geometries such as multicontact, graded Poisson, and graded Dirac geometry.
We are interested in both the geometric properties of manifolds equipped with such structures and the dynamical information that one may extract from partial differential equations arising from a multisymplectic or related geometry. These include:
- Multisymplectic and associated geometric formulations of classical field theories.
- Coisotropic embeddings and regularization.
- Symmetries and associated Noether charges.
- Darboux, or flatness, theorems.
Below you may find published and unpublished papers developed during my PhD, ordered from most recent to oldest.
Pre-prints
Read preprint (PDF)M. de León, X. Gràcia, R. Izquierdo-López, A. Martínez-Muñoz, X. Rivas, "Poisson and Jacobi structures from 2-covariant tensors".
arXiv: arXiv:2606.20030
M. de León, R. Izquierdo-López, L. Schiavone, P. Soto, "Regularization of singular time-dependent Lagrangian systems".
arXiv: arXiv:2603.24308
M. de León, R. Izquierdo-López, L. Schiavone, P. Soto, "A zoo of coisotropic embeddings".
arXiv: arXiv:2509.19039
Publications
M. de León and R. Izquierdo-López, "A description of classical field equations using extensions of graded Poisson brackets", International Journal of Geometric Methods in Modern Physics, Accepted for publication.
M. de León, R. Izquierdo-López and X. Rivas, "Brackets in Multicontact Geometry and Multisymplectization", Mediterr. J. Math. 23, 81 (2026).
M. de León and R. Izquierdo-López, "Graded poisson and graded dirac structures", J. Math. Phys. 66 (2), 022901 (2025).
DOI: 10.1063/5.0243128
M. de León and R. Izquierdo-López, "Coisotropic reduction in multisymplectic geometry", Geometric Mechanics, 1 (3), 209–244 (2024).
M. de León and R. Izquierdo-López, "A review on coisotropic reduction in symplectic, cosymplectic, contact and co-contact Hamiltonian systems", J. Phys. A: Math. Theor. 57, 163001 (2024).