Xavier Rivas

Escuela Superior en Ingeniería y Tecnología, Universidad Internacional de La Rioja

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Mathematics Genealogy Project

■ 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.

List of publications:
  1. J. de Lucas, J. Lange and X. Rivas, "A symplectic approach to Schrödinger equations in the infinite-dimensional unbounded setting". Preprint. arXiv: 2312.09192
  2. 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
  3. J. de Lucas, X. Rivas and M. Zając, "Hamiltonian stochastic Lie systems and applications". Preprint. arXiv: 2307.06232
  4. 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
  5. X. Rivas, M. Salgado and S. Souto, "Some contributions to k-contact Lagrangian field equations, symmetries and dissipation laws". Rev. Math. Phys., 2024. arXiv: 2304.00833 doi: 10.1142/S0129055X24500193
  6. 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
  7. 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
  8. 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
  9. X. Rivas, "Nonautonomous k-contact field theories". J. Math. Phys. 64(3):033507, 2023. arXiv: 2210.09166 doi: 10.1063/5.0131110
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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

Some of the colleagues I have collaborated with are: