My main research interests are differential (super)geometry and its applications to mathematical physics. I am particularly interested in symplectic, Poisson, contact, Jacobi, and similar geometric structures, as well as their applications to dynamical systems. I am also fascinated by graded manifolds and their applications to classical differential geometry and parastatistics.

In my doctoral dissertation, titled *The geometry of dissipation*,
I consider different geometric frameworks for modelling non-conservative dynamics, with a special emphasis on the aspects related to the symmetries and integrability of these systems. More specifically, three classes of geometric frameworks modeling dissipative systems are explored: systems with external forces, contact systems, and systems with impacts. During my postdoctoral period, I plan to focus my research on two main lines: integrable contact Hamiltonian systems and graded manifolds.

L. Colombo, M. de León, M. Lainz and A. López-Gordón, “Liouville-Arnold theorem for contact Hamiltonian systems”, Feb. 2023, arXiv:2302.12061 [math.SG].

L. J. Colombo, M. de León, M. E. Eyrea Irazú and A. López-Gordón, “Generalized hybrid momentum maps and reduction by symmetries of forced mechanical
systems with inelastic collisions”, June 2022, arXiv:2112.02573
[eess.SY].

L. Colombo, M. de León, M. E. Eyrea Irazú and A. López-Gordón, “Hamilton-Jacobi theory for nonholonomic and forced hybrid mechanical systems”, *Geom. Mech.* (to appear), doi: 10.1142/S2972458924500059; arXiv:2211.06252 [math-ph].

M. de León, M. Lainz, A. López-Gordón and J. C. Marrero, “A new perspective on nonholonomic brackets and Hamilton-Jacobi theory”, *J. Geom. Phys.* **198**, 105116, Feb. 2024, doi:10.1016/j.geomphys.2024.105116.

J. Gaset, A. López-Gordón and X. Rivas, “Symmetries, conservation and dissipation in time-dependent contact systems”, * Fortschr. Phys.* **71** (8-9), p. 2300048, May 2023, doi: 10.1002/prop.202300048.

M. de León, M. Lainz, A. López-Gordón and X. Rivas, “Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems”, *J. Geom. Phys.*, **187**, Feb. 2023, doi: 10.1016/j.geomphys.2023.104787.

L. J. Colombo, M. de León and A. López-Gordón, “Contact Lagrangian systems subject to impulsive constraints”, *J. Phys. A: Math. Theor.*, **55**(42), p. 425203, Oct. 2022, doi: 10.1088/1751-8121/ac96de.

M. de León, M. Lainz and A. López-Gordón, “Discrete Hamilton–Jacobi theory for systems with external forces”, *J. Phys. A: Math. Theor.*, **55**(20), p. 205201, Mar. 2022, doi: 10.1088/1751-8121/ac6240.

M. de León, M. Lainz and A. López-Gordón, “Geometric Hamilton–Jacobi theory for systems with external forces”, *J. Math. Phys.*, **63**(2), p. 022901, Feb. 2022, doi: 10.1063/5.0073214.

M.
de León, M. Lainz and A. López-Gordón, "Symmetries, constants of the motion,
and reduction of mechanical systems with external forces”, *J. Math. Phys.*, **62**(4), p. 042901, Apr. 2021, doi: 10.1063/5.0045073.

A. López-Gordón and L. J. Colombo, “On the integrability of hybrid Hamiltonian systems”, Accepted on the *Proceedings of the 8th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control*, arXiv:2307.06049 [math-ph].

M. de León, M. Lainz, A. López-Gordón and J. C. Marrero, “Nonholonomic brackets: Eden revisited”, *Geometric Science of Information. GSI 2023.* Lecture Notes in Computer Science, vol. 14072. Springer, Cham, 2023, pp. 105-112, doi: 10.1007/978-3-031-38299-4_12.

A. Anahory Simoes, A. López-Gordón, A. Bloch and L. Colombo, “Discrete Mechanics and Optimal Control for Passive Walking with Foot Slippage”, *2023 American Control Conference (ACC)*, San Diego, CA, USA, 2023, pp. 4587-4592, doi: 10.23919/ACC55779.2023.10156020.

A. López-Gordón, L. Colombo and M. de León, “Nonsmooth Herglotz variational principle”, *2023 American Control Conference (ACC)*, San Diego, CA, USA, 2023, pp. 3376-3381, doi: 10.23919/ACC55779.2023.10156228.

M.
E. Eyrea Irazú, A. López-Gordón, L. J. Colombo and M. de León, “Hybrid Routhian
reduction for simple hybrid forced Lagrangian systems”, *2022 European Control Conference (ECC)*, London, United Kingdom, 2022, doi: 10.23919/ECC55457.2022.9838077.

“The geometry of Rayleigh dissipation”, Master's Thesis, Universidad Autónoma de Madrid, July 2021, arXiv:2107.03780 [physics.class-ph].

“Study of the Entanglement Entropy of the XX Model”, Bachelor's Thesis, Universidad Complutense de Madrid, July 2020, doi: 10.13140/RG.2.2.24773.88809.

Some of the colleagues I currently collaborate or have collaborated with are:

- Alexandre Anahory Simões (School of Science and Technology, IE University, Spain)
- Leonardo J. Colombo (Centre of Automation and Robotics, CSIC, Spain)
- Manuel de León (Institute of Mathematical Sciences (CSIC) and Royal Academy of Sciences, Madrid, Spain)
- Javier de Lucas Araujo (Department of Mathematical Methods in Physics, University of Warsaw, Poland)
- Mᵃ Emma Eyrea Irazú (CONICET-CMaLP-Dept. Mathematics, UNLP, Argentina)
- Jordi Gaset (Department of Quantitative Methods, CUNEF University, Madrid, Spain)
- Katarzyna Grabowska (Department of Mathematical Methods in Physics, University of Warsaw, Poland)
- Janusz Grabowski (Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland)
- Víctor M. Jiménez (Dept. of Fundamental Mathematics, National Univ. of Distance Education, Madrid, Spain)
- Manuel Lainz (Department of Quantitative Methods, CUNEF University, Madrid, Spain)
- Juan Carlos Marrero (Dept. of Mathematics, Statistic and Operational Research, U. de La Laguna, Spain)
- Xavier Rivas (Escuela Superior en Ingeniería y Tecnología, Universidad Internacional de la Rioja, Spain)
- Bartosz M. Zawora (Department of Mathematical Methods in Physics, University of Warsaw, Poland)