■ Research
I develop my research in differential geometry and its applications to mathematical physics, mechanics and field theory. I am part of the GEOMVAP group. We collaborate with other groups, in particular with those in the Geometry, Mechanics and Control Network.
My PhD advisors were 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:
- J. de Lucas, X. Rivas and T. Sobczak, "Foundations on k-contact geometry". Preprint. arXiv: 2409.11001
- M. de León, J. Gaset, M. C. Muñoz-Lecanda, X. Rivas and N. Román-Roy, "Practical Introduction to Action-Dependent Field Theories". Preprint. arXiv: 2409.08340
- J. de Lucas, J. Lange and X. Rivas, "A symplectic approach to Schrödinger equations in the infinite-dimensional unbounded setting". Preprint. arXiv: 2312.09192 doi: 10.3934/math.20241359
- 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". Preprint. arXiv: 2311.15035
- J. de Lucas, X. Rivas and M. Zając, "Hamiltonian stochastic Lie systems and applications". Preprint. arXiv: 2307.06232
- 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 arXiv: 2306.08556 doi: 10.1007/s13398-024-01632-w
- 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
- 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
- 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
- J. Gaset, M. Lainz, A. Mas and X. Rivas, "The Herglotz variational principle for dissipative field theories". Geom. Mech. arXiv: 2211.17058 doi: 10.1142/S2972458924500060
- X. Rivas, "Nonautonomous k-contact field theories". J. Math. Phys. 64(3):033507, 2023. arXiv: 2210.09166 doi: 10.1063/5.0131110
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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: