dr. hab. Javier de Lucas Araujo, prof. UW

Department of Mathematical Methods in Physics, University of Warsaw

ul. Pasteura 5, 02-093 Warsaw, Poland

Portrait

Short Curriculum Vitae

Name: Javier de Lucas Araujo

Date and place of Birth: Talavera de la Reina (Spain) on September 2, 1981

Addressses:
 Permanent position: Department of Mathematical Methods in Physics, room 5.46, Faculty of Physics, University of Warsaw,  Pasteura 5, 02-093, Warsaw, Poland.
 Temporary position: External member at the Math-Phys Laboratorium of the Centre de Recherches Mathématiques, Universite de Montreal, Pavillon Andre-Aisenstadt, 2920, Chemin de la Tour, Montreal, QC H3T 1J4.

Email: javier.de.lucas@fuw.edu.pl

Degrees

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

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

Polish Habilitation in Physics, University of Warsaw (2017)

Spanish Habilitation: Profesor contratado doctor in Applied Mathematics, ANECA, Spain (2012)

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

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

Prizes and Distinctions  (most relevant in bold)

• 2024 - Award in recognition of achievements affecting the development and prestige of the University of Warsaw, University of Warsaw.
• 2024 - Chosen External member at the Math-Phys Laboratorium of the Centre de Recherches Mathématiques, Universite de Montreal.
• 2024 - Nomination to Didactic Award ‘Zygmunt Ajduk’ in recognition to outstanding exercises classes (Analysis II R), Faculty of Physics, University of Warsaw (Summer Semester).
 • 2023 - Individual prize of second degree for research achievements, 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 Pienkowski 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 Educacion 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 Leon council) for the best students in the Castilla y Le´ on region starting their PhD.
• 2003 - Fellowship ‘Beca de colaboración 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.

Gamma Research group


    The Geometry and Applications: Modern Mathematical Approaches (Gamma) research group is research group devoted to

  The research group is mainly led by dr. hab. J. de Lucas Araujo in the University of Warsaw, while much of the work is accomplished and supervised in collaboration with X. Rivas (University of Rovira and Virgili, Spain). The components of the group are located in the University of Warsaw:

PhD Students:

The group counts with another less formal undergraduate members accomplishing master and Bachelor theses, as well as other research works.

The group has an online weekly seminar called Gamma aimed at discussing basic and advanced research topics conducted by the Polish-Spanish geometric group gathering people from the University of Warsaw, the Universitat Rovira i Virgili and the Polytechnic University of Catalonia. The seminars are published to YouTube, having several thousands views and around 150 subscribers.

Gamma seminar YouTube Channel Gamma seminar website

Publications. Citations: 1292, Hirsch: 20 (Google scholar): Google profile

  1. M. Hontarenko, J. de Lucas, and A. Maskalaniec, A k-contact geometrical approach to pseudo-gauge transformation, submitted to JPA [arXiv] [article]
  2. A.M. Grundland, J. de Lucas, and B.M. Zawora, Stability analysis of the n-dimensional Nambu-Goto action gas models, submitted to JPA [arXiv] [article]
  3. J. de Lucas, X. Rivas, T. Sobczak, k-contact Lie systems: theory and applications, submitted to Geometric Mechanics [arXiv] [article]
  4. J. de Lucas, X. Rivas, T. Sobczak, Foundations on k-contact geometry, submitted to JGP [arXiv] [article]
  5. A. Lopez-Gordon, J. de Lucas, B.M. Zawora, Stability of contact Hamiltonian systems, 2025 [arXiv] [article]
  6. J. de Lucas, J. Lange, C. Sardon, X. Rivas, Hamilton-Jacobi equations in the k-contact setting, To be submitted, 2025 [arXiv] [article]
  7. R. Campoamor-Stursberg, O. Carballal, F.J. Herranz, J. de Lucas, Mixed superposition rules for Lie systems and compatible geometric structures, submitted to CMP [arXiv] [article]
  8. J. de Lucas, M. Zajac, Applications of standard and Hamiltonian stochastic Lie systems [arXiv] [article]
  9. J. de Lucas, J. Lange, Reduction of twisted Poisson manifolds and applications to Hamilton–Jacobi equations, To be submitted, 2025 [arXiv] [article]
  10. J. de Lucas and M. Zajac, Hamiltonian stochastic Lie systems and applications, J. Phys. A 58, 415202, 2025 [arXiv] [article]
  11. R. Campoamor-Stersberg, F.J. Herranz, J. de Lucas, Nonlinear Lie-Hamilton systems: t-Dependent curved oscillators and Kepler-Coulomb Hamiltonians, Comm. Nonl. Science Num. Sim. 152, Part B, 109206, 2026 [arXiv] [article]
  12. J. de Lucas, X. Rivas, S. Vilariño, B.M. Zawora, Marsden–Meyer–Weinstein reduction for k-contact field theories, submitted, 2025 [arXiv] [article]
  13. E. Fernandez-Saiz, J. de Lucas, M. Zajac, Hamiltonian Stochastic Lie systems and applications, J. Phys. A (2025) [arXiv] [article]
  14. A.M. Grundland, J. de Lucas, Quasi-rectifiable Lie algebras for partial differential equations, Nonlinearity, 38, 025006 (2025) [arXiv] [article]
  15. L. Colombo, J. de Lucas, X. Rivas, B. Zawora, An energy-momentum method for ordinary differential equations with an underlying k-polysymplectic manifold, J. Nonlinear Science 35, 42 (2025) [arXiv] [article]
  16. X. Gràcia, J. de Lucas, X. Rivas, N. Román-Roy, On Darboux theorems for geometric structures induced by closed forms, RACSAM 118, 131 (2024) [arXiv] [article]
  17. J. de Lucas, J. Lange, X. Rivas, A symplectic approach to Schrödinger equations in the infinite-dimensional unbounded setting, AIMS Mathematics, 2024 [arXiv] [article]
  18. J. de Lucas, A. Maskalaniec, B.M. Zawora, A cosymplectic energy-momentum method with applications, J. Nonl. Math. Phys. 31, 64 (2024) [arXiv] [article]
  19. L. Blanco, F. Jiménez, J. de Lucas, C. Sardon, Geometry preserving numerical methods for physical systems with finite-dimensional Lie algebras, J. Nonlinear Science 34, 26 (2024) [arXiv] [article]
  20. J. de Lucas, X. Rivas, S. Vilariño, B.M. Zawora, On k-polycosymplectic Marsden–Weinstein reductions, J. Geom. Phys. 191, 104899 (2023) [arXiv] [article]
  21. J. de Lucas, X. Rivas, Contact Lie systems: theory and applications, J. Phys. A 56, 335203 (2023) [arXiv] [article]
  22. L. Blanco, F. Jiménez, J. de Lucas, C. Sardon, Geometric numerical methods for Lie systems and their application in optimal control, Symmetry 15, 1285 (2023) [arXiv] [article]
  23. J. F. Cariñena, J. de Lucas, C. Sardón, Quantum quasi-Lie systems: properties and applications, EPJP 138, 339 (2023) [arXiv] [article]
  24. A.M. Grundland, J. de Lucas, Multiple Riemann wave solutions of the general form of quasilinear hyperbolic systems, Adv. Diff. Eq. 28, 73–112 (2023) [arXiv] [article]
  25. O. Esen, J. de Lucas, C. Sardon, M. Zajac, Decomposing Euler–Poincaré flow on the space of Hamiltonian vector fields, Symmetry 15, 23 (2022) [arXiv] [article]
  26. C. Gonera, J. Gonera, J. de Lucas, W. Szczesek, B.M. Zawora, More on Superintegrable Models on Spaces of Constant Curvature, Regular and Chaotic Dynamics 27, 561–571 (2022) [arXiv] [article]
  27. J. F. Cariñena, J. de Lucas, D. Wysocki, Stratified Lie systems: Theory and applications, J. Phys. A 55, 385206 (2022) [arXiv] [article]
  28. J. de Lucas, X. Gràcia, X. Rivas, N. Román-Roy, S. Vilariño, Reduction and reconstruction of multisymplectic Lie systems, J. Phys. A 55, 295204 (2022) [arXiv] [article]
  29. J. de Lucas, D. Wysocki, Darboux families and the classification of real four-dimensional indecomposable coboundary Lie bialgebras, Symmetry 13, 465 (2021) [arXiv] [article]
  30. 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) [arXiv] [article]
  31. J. de Lucas, D. Wysocki, A Grassmann and graded approach to coboundary Lie bialgebras, their classification, and Yang–Baxter equations, J. Lie Theory, 1161–1194 (2020) [arXiv] [article]
  32. J. Lange, J. de Lucas, Geometric Models for Lie–Hamilton systems on ℝ², Mathematics 7, 1053 (2019) [arXiv] [article]
  33. M.M. Lecanda, X. Gràcia, J. de Lucas, S. Vilariño, Multisymplectic structures and invariant tensors for Lie systems, J. Phys. A 52, 215201 (2019) [arXiv] [article]
  34. J.F. Cariñena, J. Grabowski, J. de Lucas, Quasi-Lie Schemes for PDEs, Int. J. Geom. Methods Mod. Phys. 16, 1950096 (2019) [arXiv] [article]
  35. J. de Lucas, C. Sardón, A Guide to Lie systems with Compatible Geometric Structures, World Scientific, Singapore, 408 pp., 2020 [arXiv] [article]
  36. A.M. Grundland, 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) [arXiv] [article]
  37. A.M. Grundland, J. de Lucas, A cohomological approach to immersion formulas via integrable systems, Selecta Mathematica (N.S.) 24, 4749–4780 (2018) [arXiv] [article]
  38. A. Ballesteros, R. Campoamor-Stursberg, E. Fernandez-Saiz, F.J. Herranz, J. de Lucas, A unified approach to Poisson–Hopf deformations of Lie–Hamilton systems based on sl(2), Springer Proc. Math. Stat. (2018) [arXiv] [article]
  39. A. Ballesteros, R. Campoamor-Stursberg, E. Fernandez-Saiz, F.J. Herranz, J. de Lucas, Poisson-Hopf algebra deformations of Lie-Hamilton systems, J. Phys. A 51, 065202 (2018) [arXiv] [article]
  40. F.J. Herranz, J. de Lucas, M. Tobolski, Lie-Hamilton systems on curved spaces: A geometrical approach, J. Phys. A 50, 495201 (2017) [arXiv] [article]
  41. M.M. Lewandowski, J. de Lucas, Geometric features of Vessiot–Guldberg Lie algebras of conformal and Killing vector fields on ℝ², Banach Center Publ. 113, 243–262 (2017) [arXiv] [article]
  42. A.M. Grundland, J. de Lucas, A Lie systems approach to the Riccati hierarchy and partial differential equations, J. Differential Equations 263, 299–337 (2017) [arXiv] [article]
  43. P. García-Estévez, F.J. Herranz, J. de Lucas, C. Sardón, Lie symmetries for Lie systems: Applications to systems of ODEs and PDEs, Appl. Math. Comp. 273, 435–452 (2016) [arXiv] [article]
  44. J. de Lucas, M. Tobolski, S. Vilariño, Geometry of Riccati equations over normed division algebras, J. Math. Anal. Appl. 440, 394–414 (2016) [arXiv] [article]
  45. J.F. Cariñena, J. de Lucas, M.F. Rañada, Jacobi multipliers, nonlocal symmetries, and harmonic oscillators, J. Math. Phys. 56, 063505 (2015) [arXiv] [article]
  46. J.F. Cariñena, J. de Lucas, Quasi–Lie families, schemes, invariants and their applications to Abel equations, J. Math. Anal. Appl. 430, 648–671 (2015) [arXiv] [article]
  47. J. de Lucas, S. Vilariño, k-symplectic Lie systems: theory and applications, J. Differential Equations 258(6), 2221–2255 (2015) [arXiv] [article]
  48. A. Ballesteros, A. Blasco, F.J. Herranz, C. Sardón, Lie–Hamilton systems on the plane: Properties, classification and applications, J. Differential Equations 258, 2873–2907 (2015) [arXiv] [article]
  49. A. Blasco, F.J. Herranz, J. de Lucas, C. Sardón, Lie–Hamilton systems on the plane: applications and superposition rules, J. Phys. A 48, 345202 (2015) [arXiv] [article]
  50. F.J. Herranz, J. de Lucas, C. Sardón, Jacobi–Lie systems: theory and low dimensional classification, DCDS-A 35, 605–614 (2015) [arXiv] [article]
  51. J.F. Cariñena, J. Grabowski, J. de Lucas, C. Sardón, Dirac–Lie systems and Schwarzian equations, J. Differential Equations 257(7), 2303–2340 (2014) [arXiv] [article]
  52. A. Ballesteros, J.F. Cariñena, F.J. Herranz, J. de Lucas, C. Sardón, From constants of motion to superposition rules for Lie–Hamilton systems, J. Phys. A 46, 285203 (2013) [arXiv] [article]
  53. J.F. Cariñena, J. de Lucas, P. Guha, A quasi-Lie schemes approach to the Gambier equation, SIGMA 9, 026 (2013) [arXiv] [article]
  54. J. Grabowski, J. de Lucas, Mixed superposition rules and the Riccati hierarchy, J. Differential Equations 254, 179–198 (2013) [arXiv] [article]
  55. J.F. Cariñena, J. de Lucas, J. Grabowski, Superposition rules for higher-order systems and their applications, J. Phys. A 45, 185202 (2012) [arXiv] [article]
  56. J. Grabowski, J. de Lucas, Mixed superposition rules and the Riccati hierarchy, J. Differential Equations 254, 179–198 (2013) [arXiv] [article]
  57. J.F. Cariñena, J. de Lucas, J. Grabowski, Superposition rules for higher-order systems and their applications, J. Phys. A 45, 185202 (2012) [arXiv] [article]
  58. J.F. Cariñena, J. de Lucas, M.F. Rañada, Un enfoque geométrico de las ecuaciones diferenciales de Abel de primera y segunda clase, Actas del XI Congreso Dr. Antonio Monteiro, 63–82 (2012) [article]
  59. J.F. Cariñena, J. de Lucas, C. Sardón, A new Lie systems approach to second-order Riccati equations, Int. J. Geom. Methods Mod. Phys. 9, 1260007 (2012) [arXiv] [article]
  60. J.F. Cariñena, J. de Lucas, A. Ramos, A geometric approach to integrability conditions for systems of ordinary differential equations, SIGMA 7, 067 (2011) [arXiv] [article]
  61. J.F. Cariñena, J. de Lucas, C. Sardón, Lie–Hamilton systems: theory and applications, Int. J. Geom. Methods Mod. Phys. 10, 1350047 (2013) [arXiv] [article]
  62. J.F. Cariñena and J. de Lucas, Superposition rules and second-order Riccati equations, J. Geom. Mech. 3, 1–22 (2011) [arXiv] [article]
  63. J.F. Cariñena and J. de Lucas, Superposition rules and second-order differential equations, in AIP Conference Proceedings 1360, 127–132 (2011) [arXiv] [article]
  64. P.G. Estevez, M.L. Gandarias, and J. de Lucas, Classical Lie symmetries and reductions of a nonisospectral Lax pair, J. Nonlinear Math. Phys. 18, 51–60 (2011) [arXiv] [article]
  65. J.F. Cariñena and J. de Lucas, Integrability of Lie systems through Riccati equations, J. Nonlinear Math. Phys. 18, 29–54 (2011) [arXiv] [article]
  66. J.F. Cariñena, J. de Lucas, and M.F. Rañada, A geometric approach to integrability of Abel differential equations, Int. J. Theor. Phys. 50, 2114–2124 (2011) [arXiv] [article]
  67. J.F. Cariñena and J. de Lucas, Lie systems: theory, generalizations, and applications, Dissertationes Math. 479, 1–169 (2011) [arXiv] [article]
  68. J.F. Cariñena, J. Grabowski, and J. de Lucas, Lie families: theory and applications, J. Phys. A 43, 305201 (2010) [arXiv] [article]
  69. R. Flores, J. de Lucas, and Y. Vorobiev, Phase splitting for periodic Lie systems, J. Phys. A 43, 205208 (2010) [arXiv] [article]
  70. J.F. Cariñena, J. de Lucas, and M.F. Rañada, Lie systems and integrability conditions for t-dependent frequency harmonic oscillators, Int. J. Geom. Methods Mod. Phys. 7, 289–310 (2010) [arXiv] [article]
  71. J.F. Cariñena and J. de Lucas, Quantum Lie systems and integrability conditions, Int. J. Geom. Meth. Mod. Phys. 6, 1235–1252 (2009) [arXiv] [article]
  72. J.F. Cariñena, P.G.L. Leach, and J. de Lucas, Quasi-Lie schemes and Emden–Fowler equations, J. Math. Phys. 50, 103515 (2009) [arXiv] [article]
  73. J.F. Cariñena, J. Grabowski, and J. de Lucas, Quasi-Lie schemes: theory and applications, J. Phys. A 42, 335206 (2009) [arXiv] [article]
  74. J.F. Cariñena and J. de Lucas, Applications of Lie systems in dissipative Milne–Pinney equations, Int. J. Geom. Methods Mod. Phys. 6, 683–699 (2009) [arXiv] [article]
  75. J.F. Cariñena, J. de Lucas, and A. Ramos, A geometric approach to time evolution operators of Lie quantum systems, Int. J. Theor. Phys. 48, 1379–1404 (2009) [arXiv] [article]
  76. J.F. Cariñena, J. de Lucas, and M.F. Rañada, Recent Applications of the Theory of Lie Systems in Ermakov Systems, SIGMA 4, 031 (2008) [arXiv] [article]
  77. J.F. Cariñena, J. de Lucas, and M.F. Rañada, Integrability of Lie systems and some of its applications in physics, J. Phys. A 41, 304029 (2008) [arXiv] [article]
  78. J.F. Cariñena and J. de Lucas, A nonlinear superposition rule for solutions of the Milne–Pinney equation, Phys. Lett. A 372, 5385–5389 (2008) [arXiv] [article]
  79. J.F. Cariñena, J. de Lucas, and A. Ramos, A geometric approach to integrability conditions for Riccati equations, Electronic Journal of Differential Equations 122, 1–14 (2007) [arXiv] [article]
  80. F. Avram, J.F. Cariñena, and J. de Lucas, A Lie systems approach for the first passage-time of piecewise deterministic processes, in Modern Trends of Controlled Stochastic Processes: Theory and Applications, Luniver Press, 2010, pp. 144–160 [arXiv] [article]
  81. J.F. Cariñena and J. de Lucas, Lie systems and integrability conditions of differential equations and some of its applications, in Differential Geometry and its Applications, World Science Publishing, Prague, 2008, pp. 407–417 [arXiv] [article]
  82. J.F. Cariñena, J. de Lucas, and M.F. Rañada, Nonlinear superpositions and Ermakov systems, in Differential Geometric Methods in Mechanics and Field Theory: Volume in Honour of W. Sarlet, Academia Press, Gent, 2007, 15–33 [arXiv] [article]

Students (past and actual)

Referee for projects

Referee for postdoc Marie-Składowska Curie actions of the Horizon program

Referee for the Fundação para a Ciência e a Tecnologia - FCT(Portugal)

Referee for the COST foundation - European Cooperation in Science and Technology

Works for students and potential collaborators

Nowadays I have several running projects. Students can request to take part in any of them so as to write Bachelor, Master, PhD dissertations or postdoc stays:

1) Lie systems, superposition rules and integrable systems,
2) Reduction methods and modern differential geometric structures,
3) Energy-momentum methods,
4) Supergeometry and super Lie group and super Lie algebra methods,
5) Orbifolds,
6) Differential geometry of differential equations: Lax pairs, Lie symmetries, properties, and applications.

News

My Facebook profile "Mathematical Physics at UW" has been by the Institute for Advanced Study (IAS, Princeton, USA).
Disclaimer: I have not been related in any manner to Symmetry or Mathematics MDPI journals for several years now. Despite my numerous petitions, my personal information is still in their website.