■ 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. Gaset, M. Lainz, A. Mas and X. Rivas, "The Herglotz variational principle for dissipative field theories". Preprint. arXiv:2211.17058
2. X. Rivas, "Nonautonomous k-contact field theories". Preprint. arXiv:2210.09166
3. M. de León, J. Gaset, M. C. Muñoz-Lecanda, X. Rivas and N. Román-Roy, "Multicontact formulation for non-conservative field theories". Preprint. arXiv:2209.08918
4. M. de León, M. Lainz, A. López-Gordón and X. Rivas, "Hamilton–Jacobi theory and integrability for autonomous and non-autonomous contact systems". Preprint. arXiv:2208.07436
5. J. de Lucas and X. Rivas, "Contact Lie systems: theory and applications". Preprint. arXiv:2207.04038
6. 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
7. M. de León, J. Gaset, X. Gràcia, M. C. Muñoz-Lecanda and X. Rivas, "Time-dependent contact mechanics". Monatsh. Math., 2022. arXiv:2205.09454 doi: 10.1007/s00605-022-01767-1
8. 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
9. 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
10. 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
11. 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
12. 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
13. 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
14. 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:

• Manuel de León
• Javier de Lucas
• Jordi Gaset
• Xavier Gràcia
• Manuel Lainz
• Asier López-Gordón
• Arnau Mas
• Miguel C. Muñoz-Lecanda
• Narciso Román-Roy
• Daniel Torres
• Silvia Vilariño

■ Teaching

Old courses

• Geometría Diferencial Aplicada. Máster Universitario en Ingeniería Matemática y Computación. Escuela Superior en Ingeniería y Tecnología, UNIR.
• Varietats diferenciables. Grau en Matemàtiques. FME, UPC.
• Càlcul. Grau en Geoinformació i Geomàtica. EPSEB, UPC.
• Fonaments matemàtics. Grau en Arquitectura Tècnica i Edificació. EPSEB, UPC.
• Informàtica. Graus en Enginyeria, àmbits industrial i TIC. EPSEVG, UPC.
• Àlgebra i geometria. Grau en Enginyeria de Sistemes Aeroespacials. EETAC, UPC.
• Àlgebra lineal i aplicacions. Grau en Enginyeria de Sistemes de Telecomunicació. EETAC, UPC.
• Càlcul en una variable. Grau en Matemàtiques. FME, UPC.
• Càlcul. Graus en Enginyeria. EEBE, UPC.