■ Research

I develop my research in differential geometry and its applications to mathematical physics, mechanics and field theory. I collaborate with many groups in the Geometry, Dynamics and Field Theory Network.

My PhD advisors were Professors Narciso Román-Roy and Xavier Gràcia Sabaté. You can find my thesis here.

I co-organize a weekly online seminar in collaboration with Professor Javier de Lucas, aimed at discussing basic and advanced research topics on Differential Geometry and Applications to Physics. For more details, visit Geometry and Applications: Modern Mathematical Approaches (Gamma).

List of publications:

1. X. Gràcia, A. Martínez-Muñoz, X. Rivas and N. Román-Roy,
   "Pairs of differential forms: a framework for precontact geometry".
   Preprint. arXiv: 2602.04882
2. X. Gràcia, X. Rivas and D. Torres,
   "Time-dependent metrics and connections".
   to appear in Geom. Mech. arXiv: 2601.14064 doi: 10.1142/S2972458926400034
3. J. de Lucas, X. Rivas and T. Sobczak,
   "k-contact Lie systems: theory and applications".
   Geom. Mech. arXiv: 2511.17734 doi: 10.1142/S2972458926400022
4. X. Gràcia, A. Martínez-Muñoz, X. Rivas and N. Román-Roy,
   "The evolution operator connecting the Lagrangian and Hamiltonian formalisms for contact systems".
   Preprint. arXiv: 2511.13401
5. X. Rivas, N. Román-Roy and A. Villanova,
   "Skinner–Rusk formalism of action-dependent multicontact field theories".
   Preprint. arXiv: 2511.01499
6. J. Gaset, X. Rivas and N. Román-Roy,
   "A survey on geometric frameworks for action-dependent classical field theories and their relationship".
   Geom. Mech. arXiv: 2506.11646 doi: 10.1142/S2972458926400010
7. M. de León, R. Izquierdo-López and X. Rivas,
   "Brackets in multicontact geometry and multisymplectization".
   Preprint. arXiv: 2505.13224
8. J. de Lucas, X. Rivas, S. Vilariño and B. M. Zawora,
   "Marsden–Meyer–Weinstein reduction for k-contact field theories".
   Preprint. arXiv: 2505.05462
9. X. Rivas, N. Román-Roy and B. M. Zawora,
   "Symmetries and Noether's theorem for action-dependent multicontact field theories".
   Lett. Math. Phys. 115(108):1-32, 2025. arXiv: 2503.03463 doi: 10.1007/s11005-025-01995-0
10. J. de Lucas, X. Rivas and T. Sobczak,
    "Foundations on k-contact geometry".
    Preprint. arXiv: 2409.11001
11. M. de León, J. Gaset, M. C. Muñoz-Lecanda, X. Rivas and N. Román-Roy,
    "Practical Introduction to Action-Dependent Field Theories".
    Fortschr. Phys. 73(5):1-25, 2025. arXiv: 2409.08340 doi: 10.1002/prop.70000
12. J. de Lucas, J. Lange and X. Rivas,
    "A symplectic approach to Schrödinger equations in the infinite-dimensional unbounded setting".
    AIMS Math. 9(10)27998-28043, 2024. arXiv: 2312.09192 doi: 10.3934/math.20241359
13. L. Colombo, J. de Lucas, X. Rivas and B. M. Zawora,
    "An energy-momentum method for ordinary differential equations with an underlying k-polysymplectic manifold".
    J. Nonlinear Sci. 35(42):1-54, 2025. arXiv: 2311.15035 doi: 10.1007/s00332-025-10135-w
14. E. Fernández-Saiz, J. de Lucas, X. Rivas and M. Zając,
    "Hamiltonian stochastic Lie systems and applications".
    J. Phys. A: Math. Theor. 58(41):415202, 2025. arXiv: 2307.06232 doi: 10.1088/1751-8121/ae0bcd
15. X. Gràcia, J. de Lucas, X. Rivas and N. Román-Roy,
    "On Darboux theorems for geometric structures induced by closed forms".
    Rev. Real Acad. Cienc. Exactas Fis. Nat. - A: Mat. 181:131, 2024. arXiv: 2306.08556 doi: 10.1007/s13398-024-01632-w
16. X. Rivas, M. Salgado and S. Souto,
    "Some contributions to k-contact Lagrangian field equations, symmetries and dissipation laws".
    Rev. Math. Phys. 36(8):2450019, 2024. arXiv: 2304.00833 doi: 10.1142/S0129055X24500193
17. J. de Lucas, X. Rivas, S. Vilariño and B. M. Zawora,
    "On k-polycosymplectic Marsden–Weinstein reductions".
    J. Geom. Phys. 191:104899, 2023. arXiv: 2302.09037 doi: 10.1016/j.geomphys.2023.104899
18. J. Gaset, A. López-Gordón and X. Rivas,
    "Symmetries, conservation and dissipation in time-dependent contact systems".
    Fortschr. Phys. 71(8-9):2300048, 2023. arXiv: 2212.14848 doi: 10.1002/prop.202300048
19. J. Gaset, M. Lainz, A. Mas and X. Rivas,
    "The Herglotz variational principle for dissipative field theories".
    Geom. Mech. 1(2):153--178, 2024. arXiv: 2211.17058 doi: 10.1142/S2972458924500060
20. X. Rivas,
    "Nonautonomous k-contact field theories".
    J. Math. Phys. 64(3):033507, 2023. arXiv: 2210.09166 doi: 10.1063/5.0131110
21. M. de León, J. Gaset, M. C. Muñoz-Lecanda, X. Rivas and N. Román-Roy,
    "Multicontact formulation for non-conservative field theories".
    J. Phys. A: Math. Theor. 56(2):025201, 2023. arXiv: 2209.08918 doi: 10.1088/1751-8121/acb575
22. 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. 187:104787, 2023. arXiv: 2208.07436 doi: 10.1016/j.geomphys.2023.104787
23. J. de Lucas and X. Rivas,
    "Contact Lie systems: theory and applications".
    J. Phys. A: Math. Theor. 56(33):335203, 2023. arXiv: 2207.04038 doi: 10.1088/1751-8121/ace0e7
24. X. Rivas and D. Torres,
    "Lagrangian–Hamiltonian formalism for cocontact systems".
    J. Geom. Mech. 15(1):1-26, 2023. arXiv: 2205.14757 doi: 10.3934/jgm.2023001
25. M. de León, J. Gaset, X. Gràcia, M. C. Muñoz-Lecanda and X. Rivas,
    "Time-dependent contact mechanics".
    Monatsh. Math. 201:1149-1183, 2023. arXiv: 2205.09454 doi: 10.1007/s00605-022-01767-1
26. J. de Lucas, X. Gràcia, X. Rivas, N. Román-Roy and S. Vilariño,
    "Reduction and reconstruction of multisymplectic Lie systems".
    J. Phys. A: Math. Theor. 55(29):295204, 2022. arXiv: 2202.13748 doi: 10.1088/1751-8121/ac78ab
27. X. Gràcia, X. Rivas and N. Román-Roy,
    "Skinner–Rusk formalism for k-contact systems".
    J. Geom. Phys. 172:104429, 2022. arXiv: 2109.07257 doi: 10.1016/j.geomphys.2021.104429
28. M. de León, J. Gaset, M. Lainz-Valcázar, X. Rivas and N. Román-Roy,
    "Unified Lagrangian–Hamiltonian formalism for contact systems".
    Fortschr. Phys. 68 (8):2000045, 2020. arXiv: 2003.13037 doi: 10.1002/prop.202000045
29. J. Gaset, X. Gràcia, M. C. Muñoz-Lecanda, X. Rivas and N. Román-Roy,
    "A k-contact Lagrangian formulation for nonconservative field theories".
    Rep. Math. Phys., 87 (3):347-368, 2021. arXiv: 2002.10458 doi: 10.1016/S0034-4877(21)00041-0
30. J. Gaset, X. Gràcia, M. C. Muñoz-Lecanda, X. Rivas and N. Román-Roy,
    "New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries".
    Int. J. Geom. Methods Mod. Phys., 17 (6):2050090, 2020. arXiv: 1907.02947 doi: 10.1142/S0219887820500905
31. J. Gaset, X. Gràcia, M. C. Muñoz-Lecanda, X. Rivas and N. Román-Roy,
    "A contact geometry framework for field theories with dissipation".
    Ann. Phys., 414:168090, 2020. arXiv: 1905.07354 doi: 10.1016/j.aop.2020.168092
32. X. Gràcia, X. Rivas and N. Román-Roy,
    "Constraint algorithm for singular field theories in the k-cosymplectic framework".
    J. Geom. Mech., 12 (1):1-23, 2020. arXiv: 1812.08487 doi: 10.3934/jgm.2020002

Collaborators:

Some of the colleagues I have collaborated with are:

• Leonardo Colombo
• Manuel de León
• Javier de Lucas
• Eduardo Fernández-Saiz
• Jordi Gaset
• Xavier Gràcia
• Rubén Izquierdo-López
• Manuel Lainz
• Julia Lange
• Asier López-Gordón
• Ángel Martínez-Muñoz
• Arnau Mas
• Miguel C. Muñoz-Lecanda
• Narciso Román-Roy
• Modesto Salgado
• Tomasz Sobczak
• Silvia Souto
• Daniel Torres
• Silvia Vilariño
• Anna Villanova
• Marcin Zając
• Bartosz M. Zawora