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
Detailed curriculum: [link]
ResearcherID: C-1498-2009
0000-0001-8643-144XDegrees
Simons-CRM Professor at the Centre de Recherches Mathématiques, Université de Montréal (2023)
Associate Professor, Faculty of Physics, University of Warsaw (2022)
Polish Habilitation in Physics, University of Warsaw (2017)[Habilitation]
Spanish Habilitation: Profesor contratado doctor in Applied Mathematics, ANECA, Spain (2012)
PhD in Physics, University of Zaragoza, Spain (2009)[PhD dissertation]
MSc in Physics, University of Salamanca, Spain (2004)
Prizes and Distinctions (most relevant in bold)
• 2026 - Invited to participate in the Workshop on Recent Developments in Symplectic Dynamics, School of Mathematics, Institute for Advanced Study, Princeton, USA (2–6 November 2026). [IAS workshop]
• 2026 - Invited seminar talk, Department of Mathematics, University of Illinois Urbana-Champaign, USA (9 November 2026).
• 2025 - Rector prize of third degree for research achievements, Faculty of Physics, University of Warsaw.
• 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 Mathématiques (CRM), University of Montreal, Canada .
• 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 recognition 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 Rector of the University of Warsaw (Natural and Mathematical Sciences Faculties).
• 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 León (Castilla y Leon council) for the best students in the Castilla y León region starting their PhD.
• 2003 - Excellences Fellowship ‘Beca de colaboración’ funded by the Ministry of Education, Culture and Sport (Spain) (2400 fellowships granted in 2004 for all students finishing their studies in all Universities in Spain).
• 1999 - One of the best scores in PAU (Prueba de acceso a la Universidad) in Castilla-La Mancha and Spain (score 9.5/10).
• 1999 - Second position in the National Mathematics Olympiad in Castilla-La Mancha and participation in the final national competition in Granada.
Gamma Research group
The Gamma Research Group, led by prof. UW Javier de Lucas Araujo at the University of Warsaw, is an internationally oriented research team advancing cutting-edge geometric methods in mathematics and mathematical physics. Our mission is to develop unifying geometric frameworks that connect differential geometry, dynamical systems, and field theory, providing both deep theoretical insight and broad applicability across disciplines.
Research Focus
We work at the intersection of:
- Geometric study of jets, symmetries, differential equations and their applications.
- Geometric mechanics and field theories, advancing geometric foundations for classical and modern dynamical systems.
- Symplectic, Poisson, contact, and generalized geometric structures, including reduction procedures and multisymplectic frameworks.
- Integrability, Lie systems, and superposition principles, developing structural approaches to non-autonomous systems and partial differential equations.
- Stochastic and numerical geometric methods, bridging geometric theory with computational and probabilistic techniques.
Research Environment and Activities
The group combines rigorous theoretical development with actively supervised PhD projects and a strong international network of collaborators. We foster a dynamic research environment through:
- An online weekly research seminar on modern geometric approaches, attracting global participation from leading experts and disseminated through widely accessed online platforms.
- A weekly hybrid reading group on Lie groupoids and Lie algebroids.
- Monographic courses on geometric mechanics in the Faculty of Physics of the University of Warsaw.
- Ongoing collaborative work with leading researchers and institutions, including the Universitat Rovira i Virgili (Spain), the Polytechnic University of Catalonia (Spain) and the Centre de Recherches Mathematiques of the University of Montreal (Canada).
- Regular involvement in international conferences and workshops in geometry and mathematical physics. Organization of conferences in the Faculty of Physics of the University of Warsaw.
Selected conference organisation and network activity
- 2024 — XVIII International Young Researchers Workshop in Geometry, Dynamics and Field Theory, University of Warsaw, Warsaw.
- 2025 — Geometric Science of Information 2025, Saint-Malo: session on geometric approaches to differential equations.
- 2026 — 2nd International Workshop on Geometric Field Theory, University of Warsaw, Warsaw, 6–8 July 2026.
- 2026 — International Workshop on k-Contact Geometry and Applications, University of Łódź, 17–18 December 2026.
- 2027 — Geometric Science of Information, Saint-Malo: session on geometric approaches to differential equations in preparation.
Impact
The group develops geometric frameworks for differential equations and field theories, including k-contact geometry, jet geometry and reduction methods. Its activities connect doctoral training, international collaboration, research publications and the Gamma Seminar.
Current members:
- X. Rivas, Universidad Rovira i Virgili, Tarragona, Spain
- S. Vilariño, University of Zaragoza, Spain
- A. Lopez-Gordon, IMPAN, Poland
- B. Zawora, KU Leuven, Belgium
- T. Sobczak, third-year PhD student
- A. Maskalaniec (with J. Grabowski), third-year PhD student
- J. Lange, PhD candidate; doctoral examination expected December 2026; thesis defence expected January 2027
- M. Wojtkowiak, second degree student
- M. Flis, second degree student
Publications. Citations: 1442 Hirsch: 22 (Google scholar): Google profile
- J.F. Carinena, J. de Lucas, Infinitesimal time reparametrisation of nonautonomous systems and its applications, 2026.
- J.F. Carinena, J. de Lucas, and M. Wojtkowiak, Contact canonoid transformations, 2026.
- J. de Lucas, Jet Bundles as Higher-Order Polarised k-Contact Manifolds, To be submitted, 2026. [arXiv]
- J. de Lucas, Classification of smooth finite-dimensional Lie algebras of vector fields on the real line, 2026.
- J. de Lucas, J. Lange, Reduction of twisted Poisson manifolds and applications to Hamilton–Jacobi equations, To be submitted, 2026.
- J. de Lucas, X. Rivas, S. Vilariño, B.M. Zawora, Marsden–Meyer–Weinstein reduction for k-contact field theories, submitted, 2026. [arXiv]
- M. Flis and J. de Lucas, Lie groupoids and Lie symmetries of differential equations, 2026.
- 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][journal]
- R. Campoamor-Stursberg, O. Carballal, F.J. Herranz, J. de Lucas, Mixed superposition rules for Lie systems, compatible geometric structures, and applications, Stud. Appl. Math. 157, e70297 (2026). [arXiv][journal]
- J. de Lucas, X. Rivas, T. Sobczak, k-contact Lie systems: theory and applications, Geometric Mechanics, 1–58 (2026). [arXiv][journal]
- J. de Lucas, J. Lange, X. Rivas, C. Sardón, Hamilton–Jacobi theory for non-conservative field theories in the k-contact framework, J. Phys. A: Math. Theor. 59, 355202 (2026). [arXiv][journal]
- J. de Lucas, M. Zajac, Applications of Standard and Hamiltonian Stochastic Lie Systems, in: F. Nielsen, F. Barbaresco (eds.), Geometric Science of Information, Lecture Notes in Computer Science, vol. 16035, Springer, Cham, 2026, pp. 354–363. [arXiv][journal]
- M. Hontarenko, J. de Lucas, and A. Maskalaniec, A k-contact geometrical approach to pseudo-gauge transformation, J. Phys. A 59, 075201 (2026). [arXiv][journal]
- J. Lange, J. de Lucas, M. Krych, A Guide to Applications of k-Contact Geometry in Dissipative Field Equations, J. Phys. A: Math. Theor. (2026), DOI: 10.1088/1751-8121/aeaf24. [arXiv][journal]
- 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][journal]
- E. Fernandez-Saiz, J. de Lucas and M. Zajac, Hamiltonian stochastic Lie systems and applications, J. Phys. A 58, 415202, 2025 [arXiv][journal]
- A.M. Grundland, J. de Lucas, Quasi-rectifiable Lie algebras for partial differential equations, Nonlinearity, 38, 025006 (2025) [arXiv][journal]
- A.M. Grundland, J. de Lucas, and B.M. Zawora, Stability analysis of the n-dimensional Nambu-Goto action gas models, J. Phys. A 58, 50 (2025). [arXiv][journal]
- A. Lopez-Gordon, J. de Lucas, B.M. Zawora, Stability of contact Hamiltonian systems, 2025.
- 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][journal]
- J. de Lucas, A. Maskalaniec, B.M. Zawora, Cosymplectic geometry, reductions, and energy-momentum methods with applications, J. Nonl. Math. Phys. 31, 64 (2024) [arXiv][journal]
- J. de Lucas, J. Lange, X. Rivas, A symplectic approach to Schrödinger equations in the infinite-dimensional unbounded setting, AIMS Mathematics, 2024 [arXiv][journal]
- 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][journal]
- 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][journal]
- J. de Lucas, X. Rivas, Contact Lie systems: theory and applications, J. Phys. A 56, 335203 (2023) [arXiv][journal]
- J. de Lucas, X. Rivas, S. Vilariño, B.M. Zawora, On k-polycosymplectic Marsden–Weinstein reductions, J. Geom. Phys. 191, 104899 (2023) [arXiv][journal]
- J. F. Cariñena, J. de Lucas, C. Sardón, Quantum quasi-Lie systems: properties and applications, EPJP 138, 339 (2023) [arXiv][journal]
- 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][journal]
- 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][journal]
- O. Esen, J. de Lucas, C. Sardon, M. Zajac, Decomposing Euler–Poincaré flow on the space of Hamiltonian vector fields, Symmetry 15, 23 (2022) [journal]
- J. F. Cariñena, J. de Lucas, D. Wysocki, Stratified Lie systems: Theory and applications, J. Phys. A 55, 385206 (2022) [arXiv][journal]
- 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][journal]
- 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][journal]
- J. de Lucas, D. Wysocki, Darboux families and the classification of real four-dimensional indecomposable coboundary Lie bialgebras, Symmetry 13, 465 (2021) [arXiv][journal]
- 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][journal]
- J. de Lucas, C. Sardón, A Guide to Lie systems with Compatible Geometric Structures, World Scientific, Singapore, 408, pp. 2020 [book]
- J.F. Cariñena, J. Grabowski, J. de Lucas, Quasi-Lie Schemes for PDEs, Int. J. Geom. Methods Mod. Phys. 16, 1950096 (2019) [arXiv][journal]
- 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][journal]
- J. Lange, J. de Lucas, Geometric Models for Lie–Hamilton systems on ℝ², Mathematics 7, 1053 (2019) [arXiv][journal]
- 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][journal]
- 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][journal]
- 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][journal]
- A.M. Grundland, J. de Lucas, A cohomological approach to immersion formulas via integrable systems, Selecta Mathematica (N.S.) 24, 4749–4780 (2018) [arXiv][journal]
- 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][journal]
- F.J. Herranz, J. de Lucas, M. Tobolski, Lie-Hamilton systems on curved spaces: A geometrical approach, J. Phys. A 50, 495201 (2017) [arXiv][journal]
- 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][journal]
- J. de Lucas, M. Tobolski, S. Vilariño, Geometry of Riccati equations over normed division algebras, J. Math. Anal. Appl. 440, 394–414 (2016) [arXiv][journal]
- 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][journal]
- 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][journal]
- 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][journal]
- 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][journal]
- J.F. Cariñena, J. de Lucas, M.F. Rañada, Jacobi multipliers, nonlocal symmetries, and harmonic oscillators, J. Math. Phys. 56, 063505 (2015) [arXiv][journal]
- J. de Lucas, S. Vilariño, k-symplectic Lie systems: theory and applications, J. Differential Equations 258(6), 2221–2255 (2015) [arXiv][journal]
- F.J. Herranz, J. de Lucas, C. Sardón, Jacobi–Lie systems: theory and low dimensional classification, DCDS-A 35, 605–614 (2015) [arXiv][journal]
- 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][journal]
- 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][journal]
- J.F. Cariñena, J. de Lucas, P. Guha, A quasi-Lie schemes approach to the Gambier equation, SIGMA 9, 026 (2013) [arXiv][journal]
- J.F. Cariñena, J. de Lucas, C. Sardón, Lie–Hamilton systems: theory and applications, Int. J. Geom. Methods Mod. Phys. 10, 1350047 (2013) [arXiv][journal]
- J. Grabowski, J. de Lucas, Mixed superposition rules and the Riccati hierarchy, J. Differential Equations 254, 179–198 (2013) [arXiv][journal]
- 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][journal]
- J.F. Cariñena, J. de Lucas, J. Grabowski, Superposition rules for higher-order systems and their applications, J. Phys. A 45, 185202 (2012) [arXiv][journal]
- 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) [journal]
- 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][journal]
- 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][journal]
- J.F. Cariñena and J. de Lucas, Superposition rules and second-order Riccati equations, J. Geom. Mech. 3, 1–22 (2011) [arXiv][journal]
- J.F. Cariñena and J. de Lucas, Lie systems: theory, generalizations, and applications, Dissertationes Math. 479, 1–169 (2011) [arXiv][journal]
- J.F. Cariñena and J. de Lucas, Integrability of Lie systems through Riccati equations, J. Nonlinear Math. Phys. 18, 29–54 (2011) [arXiv][journal]
- J.F. Cariñena and J. de Lucas, Superposition rules and second-order differential equations, in AIP Conference Proceedings 1360, 127–132 (2011) [arXiv][journal]
- 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][journal]
- 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][journal]
- 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][journal]
- J.F. Cariñena, J. Grabowski, and J. de Lucas, Lie families: theory and applications, J. Phys. A 43, 305201 (2010) [arXiv][journal]
- R. Flores, J. de Lucas, and Y. Vorobiev, Phase splitting for periodic Lie systems, J. Phys. A 43, 205208 (2010) [arXiv][journal]
- J.F. Cariñena, J. Grabowski, and J. de Lucas, Quasi-Lie schemes: theory and applications, J. Phys. A 42, 335206 (2009) [arXiv][journal]
- 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][journal]
- 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][journal]
- 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][journal]
- J.F. Cariñena and J. de Lucas, Quantum Lie systems and integrability conditions, Int. J. Geom. Meth. Mod. Phys. 6, 1235–1252 (2009) [arXiv][journal]
- 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][journal]
- 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][journal]
- 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][journal]
- 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]
- 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]
- 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][journal]
- J. de Lucas, X. Rivas, T. Sobczak, Foundations on k-contact geometry, under review in JPA [arXiv]
Students (past and current)
PhD Students: 3 defended · 1 under evaluation · 2 ongoing
- T. Sobczak, 3 year
- A. Maskalaniec (with J. Grabowski), 3 year
- J. Lange, Hamilton--Jacobi theory on k-contact manifolds and applications, PhD thesis deposited and under evaluation (2026); doctoral examination expected in December 2026; thesis defence expected in January 2027[PhD Thesis]
- B. Zawora, Marsden--Meyer--Weinstein Reduction Theories and their Applications to Energy-Momentum methods, 2026 (With distinction)[PhD Thesis]
- D. Wysocki, Geometric approaches to Lie bialgebras, their classification, and applications, 2023[PhD Thesis]
- C. Sardón-Muñoz, Lie systems, Lie symmetries and reciprocal transformations, 2015 (with distinction and Prize for doctoral theses of the University of Salamanca)[PhD Thesis]
Master's theses: 9 defended · 2 in progress
- P. Petrykowski - Cartan theory of reduction 2025/26 - in progress
- A. Surya Putra - BRST quantization 2026/27 - in progress
- T. Frelik 2025 - Complex geometry, Cartan bundles, and their applications to gauge theory
- M. Borczyńska 2025 - Marsden--Meyer--Weinstein reductions in the singular orbifold setting with applications
- T. Sobczak 2024 - New approaches to k-contact geometry and applications
- A. Maskalaniec 2024 - Super symplectic 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 [Master work]
- J. Lange 2020 - A Hamilton-Jacobi theory on twisted Poisson manifolds
- D. Wysocki 2017 - New approaches to Lie bialgebras and their quantization
- DK. Propiuk 2013 - Methods of calculation of mathematical reserves.
- DM. Napiórkowska 2013 - Geometry of the simplex method.
- Bachelor's Students: 18 defended
- D. Spisak 2026 - Introduction to the energy-Casimir method and applications [Bachelor thesis PDF]
- S. Yablonski 2026 - Symplectic Groupoids and Physical Applications. [Bachelor thesis PDF]
- M. Flis 2025 - Lie group symmetries of differential equations and applications
- J. Jurczak 2025 - Homological invariants of vector bundles and applications
- M. Wojtkowiak 2025 - Canonoid Transformations: introduction and applications
- K. Wolicki 2025 - Clifford algebras and their applications
- M. Matviienko 2024 - Mechanics on Lie Algebroids: Theory and Applications
- T. Frelik 2023 - Multisymplectic theory, reduction and applications
- M. Duch 2023 - On bk-symplectic manifolds and applications
- A. Maskalaniec 2022 - The energy-momentum method: Theory, generalisations, and applications
- W. Fabjańczuk 2017 - Supergeometric methods and applications in physics
- M. Tobolski 2015 - Riccati equations over normed division algebras with applications
- J. Szypulski 2019 - Differential geometric description of Maxwell's equations and its applications
- J. Lange 2018 - Infinite-dimensional Marsden-Weinstein reduction in quantum mechanics
- B.M. Zawora 2019 - Applications of Geometric Mechanics to the Dynamics of Asteroid Pairs
- M. Skowronek 2016 - Applications of the Marsden-Weinstein reduction in differential equations
- M. Lewandowski 2016 - Theory and applications of Lie algebras of conformal and Killing vector fields
- D. Wysocki 2015 - Algebraic and geometric methods of quantization
Research group: B.M. Zawora, J. Lange, A. Maskalaniec, T. Sobczak, X. Rivas, S. Vilariño, A. Lopez-Gordon.
Talks and slides
Invited online talk, Prague Mathematical Physics Seminar, Mathematical Institute, Charles University, Prague, Czech Republic, 1 October 2026. A k-contact description of jet geometry, PDEs, and related techniques.
Invited talk, Geometry and Differential Equations Seminar, Institute of Mathematics of the Polish Academy of Sciences (IMPAN), Warsaw, Poland, 28 October 2026. A k-contact approach to finite-order jet bundles and PDEs
Invited seminar talk, Department of Mathematics, University of Illinois Urbana-Champaign, Urbana-Champaign, USA, 9 November 2026.
Invited participant, Workshop on Recent Developments in Symplectic Dynamics, School of Mathematics, Institute for Advanced Study, Princeton, USA, 2–6 November 2026. [IAS workshop]
Invited plenary talk, XXXIV International Fall Workshop on Geometry and Physics, Universitat Rovira i Virgili, Tarragona, Spain, 1–4 September 2026. A k-contact description of finite-dimensional jet geometry. [PDF]
Invited plenary talk, XLIII Workshop on Geometric Methods in Physics, University of Białystok, Białystok, Poland, 29 June–4 July 2026. Introduction to k-contact geometry and applications. [PDF]
Invited seminar talk, Seminar on Differential Geometry and its Applications, Mathematical Institute, Silesian University in Opava, Opava, Czech Republic, 4 December 2025. Applications of quasi-rectifiable Lie algebras to hydrodynamic-type systems.
Talk in a thematic session, 7th International Conference on Geometric Science of Information (GSI 2025), Palais du Grand Large, Saint-Malo, France, 29–31 October 2025 (talk delivered on 29 October 2025). Applications of standard and Hamiltonian stochastic Lie systems.
Online seminar talk, Gamma Seminar, Faculty of Physics, University of Warsaw, Warsaw, Poland, 23 October 2025. Lie systems: A 16-year retrospective on a 132-year-old theory. [PDF]
Referee for projects and expert evaluation
Expert evaluator for the Marie Skłodowska-Curie Actions Postdoctoral Fellowships (MSCA-PF), European Research Executive Agency, 2025–2026.
Completed the European Research Executive Agency (REA) online course MSCA-PF Proposals' Evaluation: Process, Evaluation Criteria, and Best Practice for experts appointed to evaluate the MSCA-PF-2026 call; certificate issued 2 October 2026.
Referee for the Fundação para a Ciência e a Tecnologia - FCT (Portugal)
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.
Useful links
Website with materials for my lectures [link]
Link to the Faculty of Physics of the University of Warsaw structure [link]
Link to Xavier Rivas website [link]
Link to Bartosz Zawora website [link]
MR Look up [link]
Description of Journals [link]
News
My Facebook profile "Mathematical Physics at UW" has been by the Institute for Advanced Study (IAS, Princeton, USA).
- B. Zawora obtained a NAWA grant to work in KU Leuven, Belgium.
- J. Lange obtained one of the didactic distinctions in 2026 for her exercise lectures in the Faculty of Physics of the University of Warsaw.
- Fundacja Uniwersytetu Warszawskiego financially supported my session "A geometric approach to differential equations" organised in the conference Geometric Science of Information held in Saint-Malo, France on October 29–31, 2025.
- The work by B.M. Zawora and J. Lange obtained one of the eight prizes given for more than two-hundred participants in the conference GSI, France, 29-31 October, 2025 (Saint-Malo).
- A. Maskalaniec obtained one of the prizes for the best posters for "k-Contact geometry and pseudo-gauge invariance in relativistic spin hydrodynamics" in the conference XXXIII International Fall Workshop on Geometry and Physics, held from September 09 to 12, 2025, in Córdoba, Spain.
- J. Lange obtained one of the didactic distinctions in 2025 for her exercise lectures in the Faculty of Physics of the University of Warsaw.
- J. de Lucas obtained one of the didactic distinctions in 2025 for her exercise lectures in the Faculty of Physics of the University of Warsaw.
- 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 the website of Symmetry (Mathematics accepted to delete my information after many attempts).
Hojas de ejercicios
This protected catalogue collects analysis exercise PDFs from the Grezio directory, with local copies stored in this GitHub Pages repository.