■ 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:
- X. Rivas and D. Torres
"Lagrangian–Hamiltonian formalism for time-dependent dissipative mechanical systems"
Preprint. arXiv:2205.14757
- M. de León, J. Gaset, X. Gràcia, M. C. Muñoz-Lecanda and X. Rivas
"Time-dependent contact mechanics"
Preprint. arXiv:2205.09454
- 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"
Fortschritte der 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 formalism for field theories with dissipation"
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: