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

Department of Mathematical Methods in Physics, University of Warsaw,

ul Pasteura 5, 02.093, Warsaw, Poland.

Short Curriculum Vitae

Name: Javier de Lucas Araujo

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

Addresses:
 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 Hanilitation: 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 Distintions  (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 researcg 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). 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.

Publications (last 10 years). Citations: 1244, Hirsch: 20 (According to Google scholar).

  1. R. Campoamor-Stersberg, F.J. Herranz, J. de Lucas,  Nonlinear Lie-Hamilton systems: $t$-Dependent curved oscillators and Kepler-Coulomb Hamiltonians, submitted, 2025, arXiv:2505.13853
  2. A. Lopez-Gordon, J. de Lucas, B.M. Zawora, Stabillity of contact Hamiltonian systems, 2025.
  3. J. de Lucas, J. Lange, C. Sardon, X. Rivas, Hamilton-Jacobi equations in thte k-contact setting, To be submitted, 2025.
  4. J. de Lucas, J. Lange, Reduction of twisted Poisson manifolds and applications to Hamilton–Jacobi equations. To be submitted, 2025.
  5. J. de Lucas, X. Rivas, S. Vilariño, B.M. Zawora, Marsden--Meyer--Weinstein reduction for k-contact field theories . submitted, 2025, arXiv:2505.05462
  6. E. Fernandez-Saiz, J. de Lucas, M. Zajac, Hamiltonian Stochastic Lie systems and applications, 2025, arXiv:2307.06232
  7. A.M. Grundland, J. de Lucas, and B.M. Zawora, Stability analysis of the -dimensional Nambu-Goto action gas models,
  8. J. de Lucas, X. Rivas, T. Sobczak, Foundations on k-contact geometry, submitted. ArXiv
  9. A.M. Grundland, J.  de Lucas, Quasi-rectifiable Lie algebras for partial differential equations, Nonlinearity,38, 025006 ( 2025). Nonlinearity  ariv:2312.05238
  10. 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, 2024. https://arxiv.org/abs/2311.15035
  11. J. de Lucas, J. Lange, X. Rivas, A symplectic approach to Schrodinger equations in the infinite-dimensional unbounded setting, AIMS Mathematics, 2024. https://arxiv.org/abs/2312.09192 https://www.aimspress.com/article/id/66f6a53fba35de7eae90727f
  12. J. de Lucas, A. Maskalaniec, and B.M. Zawora. A cosymplectic energy-momentum method with applications, J. Nonl. Math. Phys. 31, 64 (2024). https://A cosymplectic energy-momentum method with applications,
  13. 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). https://link.springer.com/article/10.1007/s00332-023-10000-8
  14. J. de Lucas, X. Rivas, S. Vilariño, B.M. Zawora, On k-polycosymplectic Marsden-Weinstein reductions, J. Geom. Phy. 191, 104899 (2023).
  15. J. de Lucas, X. Rivas, Contact Lie systems: theory and applications, J. Phys. A 56, 335203 (2023).
  16. L. Blanco, F. Jime ́nez, J. de Lucas, C. Sardon, Geometric numerical methods for Lie systems and their application in optimal control, Symmetry 15, 1285 (2023).
  17. J. F. Cariñena, J. de Lucas, C. Sardón, Quantum quasi-Lie systems: properties and applications, EPJP 138, 339 (2023).
  18. 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).
  19. O. Esen, J. de Lucas, C. Sardon, and M. Zajac, Decomposing Euler-Poincare flow on the space of Hamiltonian vector fields, Symmetry 15, 23 (2022).
  20. J. de Lucas, D. Wysocki, Darboux families and the classification of real four-dimensional indecomposable coboundary Lie bialgebras, Symmetry 13, 465 (2021).
  21. 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).
  22. 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.
  23. J. Lange and J. de Lucas, Geometric Models for Lie–Hamilton systems on R2, Mathematics 2019, 7, 1053, (2019).
  24. M.M. Lecanda, X. Gracia, J. de Lucas, and S. Vilarino, Multisymplectic structures and invariant tensors for Lie systems, J. Phys. A, 52, 215201, (2019).
  25. J.F. Cariñena, J. Grabowski, and J. de Lucas, Quasi-Lie Schemes for PDEs, Int. J. Geom. Methods. Mod. Phys. 16, 1950096 (2019).
  26. J. de Lucas, C. Sardo ́n, A Guide to Lie systems with Compatible Geometric Structures, World Scientific, Singapore, 408 pp., 2020.
  27. 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).
  28. A.M. Grundland and J. de Lucas, A cohomological approach to immersion formulas via integrable systems, Selecta Mathematica - New Series 24, 4749–4780 (2018).
  29. 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).
  30. 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).
  31. F.J. Herranz, J. de Lucas, M. Tobolski Lie-Hamilton systems on curved spaces: A geometrical approach, J. Phys. A 50, 495201 (2017).
  32. 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).
  33. F.J. Herranz, J. de Lucas and M. Tobolski, Lie-Hamilton systems on curved spaces: A geometrical approach, J. Phys. A 50, 495201 (2017)
  34. 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).
  35. F.J. Herranz, J. de Lucas, and M. Tobolski, Lie-Hamilton systems on curved spaces: A geometrical approach, J. Phys. A 50, 495201 (2017).
  36. 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).
  37. 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).
  38. 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).
  39. J. de Lucas, M. Tobolski, and S. Vilariño, Geometry of Riccati equations over normed division algebras, J. Math. Anal. Appl. 440, 394–414 (2016).
  40. J.F. Cariñena, J. de Lucas, and M.F. Rañada, Jacobi multipliers, nonlocal symmetries, and harmonic oscillators, J. Math. Phys. 56, 063505 (2015).
  41. 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).
  42. J. de Lucas and S. Vilariño, k-symplectic Lie systems: theory and applications, J. Differential Equations 258 (6), 2221–2255 (2015).
  43. 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).
  44. 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).
  45. 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).
  46. 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.
  47. 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).
  48. 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).
  49. F.J. Herranz, J. de Lucas, and C. Sardón, Jacobi--Lie systems: theory and low dimensional classification, Accepted in Proceedings AIMS (2015). [Arxiv]
  50. 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]
  51. J. de Lucas and S. Vilariño, k-symplectic Lie systems: theory and applications, J. Differential Equations 258 (6), 2221--2255 (2015). [Arxiv]
  52. 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]
  53. 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]
  54. 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]
  55. J. de Lucas and C. Sardón, On Lie systems and Kummer-Schwarz equations, J. Math. Phys. 54, 033505 (2013). [Arxiv]
  56. 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]
  57. J.F. Cariñena, J. de Lucas, and P. Guha, A quasi-Lie schemes approach to the Gambier equation, SIGMA 9, 026 (2013). [Arxiv]
  58. J. Grabowski and J. de Lucas, Mixed superposition rules and the Riccati hierarchy, J. Diff. Equ. 254, 179--198 (2013). [Arxiv]
  59. 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]
  60. 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).
  61. 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).
  62. 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]
  63. 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]
  64. 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]
  65. J. de Lucas and C. Sardón, On Lie systems and Kummer–Schwarz equations, J. Math. Phys. 54, 033505 (2013). [Arxiv]
  66. 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]

    • Students (past and actual)

    • PhD Students:

      • T. Sobczak, 1 year
      • A. Maskalaniec (with J. Grabowski), 1 year
      • J. Lange, planned 2026
      • B. Zawora, planned 2025
      • D. Wysocki, Geometric approaches to Lie bialgebras, their classification, and applications, 2023
      • C. Sardón-Muñoz, Lie systems, Lie symmetries and reciprocal transformations, 2015 (Doctoral prize of the Faculty of Physics of the University of Salamanca)

    • Master's Students

      • T. Frelik 2024/25 -  Cartan Theory on infinite-dimensional manifolds - In progress
      • M. Borczyńska 2024/25 - Regular and singular symplectic reduction on orbifolds - In progress
      • T. Sobczak 2024 - New approaches to k-contact geometry and applications
      • A. Maskalaniec 2024 -  Supersymplectic geometry and reductions
      • B.M. Zawora 2021 - A time-dependent energy-momentum method - Prize Joanny Gwizdow i Jerzy Glazer of the Faculty of Physics of the University of Warsaw
      • J. Lange 2020 - A Hamilton-Jacobi theory on twisted Poisson manifolds
      • D. Wysocki  2017 - New approaches to Lie bialgebras and their quantization
      • K. Propiuk 2013 - Methods of calculation of mathematical reserves.
      • M. Napiórkowska 2013 - Geometry of the simplex method
    • Bachelor's Students:
      • M. Flis, Symmetries of Differential equations and applications - 2025 - in progress
      • J. Jurczak,  Homological invariants of vector bundles and applications - 2025 - in progress
      • K. Wolicki, Clifford algebras and applications - 2025 - in progress
      • M. Matviienko - Mechanics on Lie Algebroids: Theory and Applications - 2024
      • T. Frelik - Multisymplectic theory, reduction and applications - 2023
      • M. Duch -  On b^k-symplectic manifolds and applications - 2023
      • W. Fabjanczuk - Metody supergeometryczne i zastosowania w fizyce - 2017
      • M. Tobolski - Riccati equations over normed division algebras with applications - 2015
      • J. Szypulksi - Opis równań Maxwella w geometrii różniczkowej i ich zastosowania - 2019
      • J. Lange - Infinite-dimensional Marsden-Weinstein reduction in quantum mechanics - 2018
      • B.M. Zawora - Zastosowania mechaniki geometrycznej w badaniu dynamiki asteroir - 2019
      • M. Skowronek -  Zastosowania redukcji Marsdena-Weinsteina w równaniach różniczkowych fizyki - 2016
      • M. Lewandowski - Teoria i zastosowania algebr Liego pól wektorowych konforemnych i Killinga - 2016
      • D. Wysocki - Algebraiczny i geometryczne metody kwantyzacji - 2015

      Research group: B.M. Zawora, J. Lange, A. Maskalaniec, T. Sobczak, M. Borczyńska, X. Rivas, S. Vilarino.

    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.

    News

    My Facebook profile "Mathematical Physics at UW" has been by the Institute for Advanced Study (IAS, Princeton, USA).