Short Curriculum Vitae

Degrees and positions

Simons-CRM Professor at the Center de Recherchers Mathematiques, University of Montreal (2023)

Associate Professor at the Faculty of Physics, University of Warsaw (2022)

Polish Habilitation in Physics (2017)

Profesor contratado doctor, ANECA, Spain (2012)

PhD in Physics, University of Zaragoza, Spain (2009)

MSc in Physics, University of Salamanca, Spain (2004)

Prizes

• 2023 - Individual prize of second degree for research acievements, Faculty of Physics, University of Warsaw.
• 2023 - Simons–CRM Professorship, Centre de Recherches Mathematiques (CRM), University of Montreal, Canada (one of the most reputable research positions at the CRM).
• 2022 - Nomination to Didactic Award ‘Zygmunt Ajduk’ in recognition to outstanding exercises classes (Analysis III Special Functions in Mathematical Physics), Faculty of
Physics, University of Warsaw (Summer Semester).
• 2021 - Dean Prize of third degree for research achievements.2021 - Dean Prize in commemoration to Rector Stefan Pie´ nkowski and Rector Grzegorz Białkowski for the best researcher in the Faculty of Physics of the University of Warsaw (younger than 40 years old).
• 2020 - UW Rector Prize of second degree in recognition to the publication “A Guide to Lie Systems with Compatible Geometric Structures”, research on the differential geometry properties of differential equations, and didactic achievements, University of Warsaw.
• 2020 - UW Didactic Award ’Zygmunt Ajduk’ in reocgnition to outstanding exercises classes (Differential Geometry), Faculty of Physics, University of Warsaw.
• 2019 - Award in recognition of achievements affecting the development and prestige of the University of Warsaw, University of Warsaw.
• 2018 - Nomination to the best paper prize of the conference ,,10th International Symposium on Quantum theory and symmetries and 12th International Workshop on Lie
Theory and Its Applications in Physics”(+70 participants).
• 2017 - Didactic Award of the Dean of the University of Warsaw.
• 2016 - Award in recognition of achievements affecting the development and prestige of the University of Warsaw, University of Warsaw.
• 2015 - Individual prize of third degree, Faculty of Physics, University of Warsaw.
• 2014 - Best teacher of the Faculty of Physics, University of Warsaw (UW Student council).
• 2013 - Didactic Award for outstanding classes and lectures, Summer term, University of Warsaw.
• 2011 - Postdoc fellowship for young researchers, IMPAN.
• 2011 - Special Award for Doctoral Theses, University of Zaragoza, year 2009/2010.
• 2010 - Postdoc fellowship for young researchers, IMPAN.
• 2009 - Postdoc fellowship for young researchers, IMPAN.
• 2006 - F.P.U. Fellowship funded by the Ministerio de Educaci´ on y Ciencia (Ministry of Education and Science) for the best students in Spain to accomplish my PhD thesis project “Lie systems and applications to Quantum Mechanics”.
• 2005 - Fellowship funded by the Faculty of Science of the University of Salamanca for the best students in the University of Salamanca starting their PhD.
• 2005 - F.P.I. Fellowship funded by the Junta de Castilla y Le´ on ( Castilla y Le´ on council) for the best students in the Castilla y Le´ on region starting their PhD.
• 2003 - Fellowship ‘Beca de colaboraci´ on’ funded by the Ministry of Education, Culture and Sport (Spain) and granted by the Faculty of Science of the University of Salamanca for the best (5) students of the Faculty of Physics of the University of Salamanca in the period from 1999 to 2003.

Main publications (last 10 years)

• J. de Lucas, J. Lange, X. Rivas, A symplectic approach to Schrodinger equations in the infinite-dimensional unbounded setting, arXiv:2312.09192, submitted to AIMS Mathematics, 2024.

• A.M. Grundland, J. de Lucas, Almost rectifiable Lie algebras and k-wave solutions of nonlinear hydrodynamic-type systems, arXiv:2312.05238, submitted to Nonlinearity, 2024.
• L. Colombo, J. de Lucas, X. Rivas, B. Zawora, An energy-momentum method for ordinary differential equations with an underlying k-polysymplectic manifold, arXiv:2311.15035, submitted to Journal of Nonlinear Science, 2024.
• J. de Lucas, A. Maskalaniec, and B.M. Zawora. A cosymplectic energy-momentum method with applications, arXiv:2302.05827, submitted to Journal of Nonlinear Mathematical Physics (2024).
• L. Blanco, F. Jimenez, J. de Lucas, C. Sardon, Geometry preserving numerical methods for physical systems with finite-dimensional Lie algebras, J. Nonlinear Science 34, 26 (2024).
• J. de Lucas, X. Rivas, S. Vilarino, B.M. Zawora, On k-polycosymplectic Marsden-Weinstein reductions, J. Geom. Phy. 191, 104899 (2023).
• J. de Lucas, X. Rivas, Contact Lie systems: theory and applications, J. Phys. A 56, 335203 (2023).
• L. Blanco, F. Jime ́nez, J. de Lucas, C. Sardo ́n, Geometric numerical methods for Lie systems and their application in optimal control, Symmetry 15, 1285 (2023).
• J. F. Carin ̃ena, J. de Lucas, C. Sardo ́n, Quantum quasi-Lie systems: properties and applications, EPJP 138, 339 (2023).
• A.M. Grundland and J. de Lucas, Multiple Riemann wave solutions of the general form of quasilinear hyperbolic systems, Adv. Diff. Eq. 28, 73–112 (2023).
• O. Esen, J. de Lucas, C. Sardon, and M. Zaja ̧c, Decomposing Euler-Poincare flow on the space of Hamiltonian vector fields, Symmetry 15, 23 (2022).
• J. de Lucas, D. Wysocki, Darboux families and the classification of real four-dimensional indecomposable coboundary Lie bialgebras, Symmetry 13, 465 (2021).
• A. Ballesteros, R. Campoamor-Stursberg, E. Fernandez-Saiz, F.J. Herranz, J. de Lucas, Poisson-Hopf deformations of Lie-Hamilton systems revisited: deformed superposition rules and applications to the oscillator algebra, J. Phys. A 54, 205202 (2021).
• J. de Lucas and D. Wysocki, A Grassmann and graded approach to coboundary Lie bialgebras, their classification, and Yang-Baxter equations, J. Lie Theory 2020, 1161–1194.
• J. Lange and J. de Lucas, Geometric Models for Lie–Hamilton systems on R2, Mathematics 2019, 7, 1053, (2019).
• M.M. Lecanda, X. Gracia, J. de Lucas, and S. Vilarin ̃o, Multisymplectic structures and invariant tensors for Lie systems, J. Phys. A, 52, 215201, (2019).
• J.F. Carin ̃ena, J. Grabowski, and J. de Lucas, Quasi-Lie Schemes for PDEs, Int. J. Geom. Methods. Mod. Phys. 16, 1950096 (2019).
• J. de Lucas, C. Sardo ́n, A Guide to Lie systems with Compatible Geometric Structures, World Scientific, Singapore, 408 pp., 2020.
• A.M. Grundland and J. de Lucas,On the geometry of the Clairin theory of conditional symmetries for higher-order systems of PDEs with applications, Diff. Geom. Appl. 67, 101557 (2019).
• A.M. Grundland and J. de Lucas, A cohomological approach to immersion formulas via integrable systems, Selecta Mathematica - New Series 24, 4749–4780 (2018).
• A. Ballesteros, R. Campoamor-Stursberg, E. Fernandez-Saiz, F.J. Herranz and J. de Lucas, A unified approach to Poisson–Hopf deformations of Lie–Hamilton systems based on sl(2), accepted in “Springer Proceedings in Mathematics, Statistics” (2018).
• A. Ballesteros, R. Campoamor-Stursberg, E. Fernandez-Saiz, F.J. Herranz and J. de Lucas, Poisson-Hopf algebra deformations of Lie-Hamilton systems, J. Phys. A 51, 065202 (2018).
• F.J. Herranz, J. de Lucas, M. Tobolski Lie-Hamilton systems on curved spaces: A geometrical approach, J. Phys. A 50, 495201 (2017).
• A. Ballesteros, R. Campoamor-Stursberg, E. Fernandez-Saiz, F.J. Herranz and J. de Lucas, Poisson-Hopf algebra deformations of Lie-Hamilton systems, J. Phys. A 51, 065202 (2018).
• F.J. Herranz, J. de Lucas and M. Tobolski, Lie-Hamilton systems on curved spaces: A geometrical approach, J. Phys. A 50, 495201 (2017)
• A. Ballesteros, R. Campoamor-Stursberg, E. Fernandez-Saiz, F.J. Herranz, and J. de Lucas, Poisson-Hopf algebra deformations of Lie-Hamilton systems, J. Phys. A 51, 065202 (2018).
• F.J. Herranz, J. de Lucas, and M. Tobolski, Lie-Hamilton systems on curved spaces: A geometrical approach, J. Phys. A 50, 495201 (2017).
• M.M. Lewandowski and J. de Lucas, Geometric features of Vessiot–Guldberg Lie algebras of conformal and Killing vector fields on R₂, Banach Center Publications 113, 243–262 (2017).
• A.M. Grundland and J. de Lucas, A Lie systems approach to the Riccati hierarchy and partial differential equations, J. Differential Equations 263, 299–337 (2017).
• P. Garcia-Estevez, F.J. Herranz, J. de Lucas, and C. Sardón, Lie symmetries for Lie systems: Applications to systems of ODEs and PDEs, Appl. Math. Comp. 273, 435–452 (2016).
• J. de Lucas, M. Tobolski, and S. Vilariño, Geometry of Riccati equations over normed division algebras, J. Math. Anal. Appl. 440, 394–414 (2016).
• J.F. Cariñena, J. de Lucas, and M.F. Rañada, Jacobi multipliers, nonlocal symmetries, and harmonic oscillators, J. Math. Phys. 56, 063505 (2015).
• J.F. Cariñena and J. de Lucas, Quasi–Lie families, schemes, invariants and their applications to Abel equations, J. Math. Anal. Appl. 430, 648–671 (2015).
• J. de Lucas and S. Vilariño, k-symplectic Lie systems: theory and applications, J. Differential Equations 258 (6), 2221–2255 (2015).
• A. Ballesteros, A. Blasco, F.J. Herranz, and C. Sardón, Lie–Hamilton systems on the plane: Properties, classification and applications, J. Differential Equations 258, 2873–2907 (2015).
• A. Blasco, F.J. Herranz, J. de Lucas, and C. Sardón, Lie–Hamilton systems on the plane: applications and superposition rules, J. Phys. A 48, 345202 (2015).
• J. de Lucas, M. Tobolski, and S. Vilariño, A new application of k-symplectic Lie systems, Int. J. Geom. Methods Mod. Phys. 12, 1550071 (2015).
• F.J. Herranz, J. de Lucas, and C. Sardón, Jacobi–Lie systems: theory and low dimensional classification, in: The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, 2015. Discrete Contin. Dyn. Syst. Series A, 605–614, 2015.
• P.G. Estevez, F.J. Herranz, J. de Lucas, and C. Sardón, Lie symmetries for Lie systems: applications of ODEs and HODEs, Appl. Math. Comp. 273, 435–452 (2015).
• J.F. Cariñena and J. de Lucas, Quasi-Lie families, quasi-Lie schemes, and their applications to Abel equations, J. Math. Anal. Appl. 430, 648–671 (2015).
• F.J. Herranz, J. de Lucas, and C. Sardón, Jacobi--Lie systems: theory and low dimensional classification, Accepted in Proceedings AIMS (2015). [Arxiv]
• J. de Lucas, M. Tobolski, and S. Vilarino, A new application of k-symplectic Lie systems, Int. J. Geom. Methods Mod. Phys. 12, 1550071 (2015). [Arxiv]
• J. de Lucas and S. Vilariño, k-symplectic Lie systems: theory and applications, J. Differential Equations 258 (6), 2221--2255 (2015). [Arxiv]
• A. Ballesteros, A. Blasco, J.F. Herranz, J. de Lucas, and C. Sardón, Lie-Hamilton systems on the plane: theory, classification and applications, J. Differential Equations 258, 2873--2907 (2015). [Arxiv]
• J.F. Cariñena, J. Grabowski, J. de Lucas, and C. Sardón, Dirac-Lie systems and Schwarzian equations, J. Differential Equations 257 (7), 2303--2340 (2014). [Arxiv]
• A. Ballesteros, J.F. Cariñena, F.J. Herranz, J. de Lucas, and C. Sardón, From constants of motion to superposition rules for Lie-Hamilton systems, J. Phys. A: Math. Theor. 46, 285203 (2013). [Arxiv]
• J. de Lucas and C. Sardón, On Lie systems and Kummer-Schwarz equations, J. Math. Phys. 54, 033505 (2013). [Arxiv]
• J.F. Cariñena, J. de Lucas, and C. Sardón, Lie-Hamilton systems: theory and applications, Int. J. Geom. Methods Mod. Phys. 10, 09129823 (2013). [Arxiv]
• J.F. Cariñena, J. de Lucas, and P. Guha, A quasi-Lie schemes approach to the Gambier equation, SIGMA 9, 026 (2013). [Arxiv]
• J. Grabowski and J. de Lucas, Mixed superposition rules and the Riccati hierarchy, J. Diff. Equ. 254, 179--198 (2013). [Arxiv]
• J.F. Cariñena, J. de Lucas, and J. Grabowski, Superposition rules for higher-order systems and their applications, J. Phys. A: Math. Theor. 45, 185202 (2012). [Arxiv]
• J.F. Cariñena, J. de Lucas, and M.F. Rañada, Un enfoque geométrico de las ecuaciones diferenciales de Abel de primera y segunda clase, Actas del XI Congreso del Dr. Antonio Monteiro 2011, 63--82 (2012).
• J.F. Cariñena, J. de Lucas, and C. Sardón, A new Lie systems approach to second-order Riccati equations, Int. J. Geom. Methods Mod. Phys. 9, 1260007 (2012).
• J.F. Cariñena, J. de Lucas, and A. Ramos, A geometric approach to integrability conditions for systems of ordinary differential equations, SIGMA 7, 067 (2011). [Arxiv]
• J.F. Cariñena, J. de Lucas, and C. Sardón, Lie–Hamilton systems: theory and applications, Int. J. Geom. Methods Mod. Phys. 10, 1350047 (2013). [Arxiv]
• J.F. Cariñena, J. de Lucas, and C. Sardón, Lie–Hamilton systems on the plane: Properties, classification and applications, J. Phys. A: Math. Theor. 46, 285203 (2013). [Arxiv]
• J. de Lucas and C. Sardón, On Lie systems and Kummer–Schwarz equations, J. Math. Phys. 54, 033505 (2013). [Arxiv]
• J.F. Cariñena, J. de Lucas, and C. Sardón, Lie–Hamilton systems: theory and applications, Int. J. Geom. Methods Mod. Phys. 10, 1350047 (2013). [Arxiv]