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Contact me

Room 3.50, ul. Pasteura 5, 02-093 Warsaw (Poland).

E-mail: g (NO SPACE) moreno (AT) fuw.edu.pl

Phone: +48 22 55 32 750

Dydaktyka Selected Publications

Research

General Interests

My area is Geometry of Nonlinear Partial Differential Equations. I obtain results about the structure and the classification of nonlinear PDEs by using: jet spaces, classical projective geometry, differential geometry and topology, homological and commutative algebra, representation theory. Other interests include: geometric mechanics, differential calculus over (graded) commutative algebras, field theory, general relativity, group actions on geometric structures, variational problems and variational sequences.

Selected Publications

  1. Invariant Monge-Ampère equations on contactified para-Kähler manifolds. Dmitri Alekseevsky, Gianni Manno, Giovanni Moreno; preprint (2024).
  2. Third-order affine-invariant (systems of) PDEs in two independent variables as vanishing of the Fubini-Pick invariant. Dmitri V. Alekseevsky, Gianni Manno, Giovanni Moreno; preprint (2024).
  3. Projectively and affinely invariant PDEs on hypersurfaces. Dmitri V. Alekseevsky, Gianni Manno, Giovanni Moreno; Proceedings of the Edinburg Mathematical Society (accepted 22.03.2024).
  4. The moment map on the space of symplectic 3D Monge-Ampère equations. Jan Gutt, Gianni Manno, Giovanni Moreno, Robert Śmiech; Advances in Differential Equations, 29(7-8) (2024).
  5. A general method to construct invariant PDEs on homogeneous manifolds . Dmitri V. Alekseevsky, Jan Gutt, Gianni Manno, Giovanni Moreno; Communications in Contemporary Mathematics, 24(3) (2022).
  6. Complex contact manifolds, varieties of minimal rational tangents, and exterior differential systems. Jarosław Buczyński, Giovanni Moreno; Banach Center Publications, 117 (2019) 145-176.
  7. Geometry of Lagrangian Grassmannians and Nonlinear PDEs. Jan Gutt, Gianni Manno, Giovanni Moreno; Banach Center Publications, 117 (2019) 9–44.
  8. Lowest degree invariant 2nd order PDEs over rational homogeneous contact manifolds. Dmitri Alekseevsky, Jan Gutt, Gianni Manno, Giovanni Moreno; Communications in Contemporary Mathematics, 21(1) (2019) 54 pages.
  9. Contact manifolds, Lagrangian Grassmannians and PDEs. Olimjon Eshkobilov, Gianni Manno, Giovanni Moreno, Katja Sagerschnig; Complex Manifolds, 5 (2018) 26-88.
  10. An introduction to completely exceptional 2nd order scalar PDEs. Giovanni Moreno; Banach Centre Publications, 113 (2017) 275-289.
  11. On a geometric framework for Lagrangian Supermechanics. J. A. Bruce, K. Grabowska, G. Moreno; Journal of Geometric Mechanics 9(4), 411–437 (2017).
  12. Geometry of the free–sliding Bernoulli beam. G. Moreno, M. E. Stypa; Communications in Mathematics 24 (2016) 153–171.
  13. On the vertex–to–edge duality between the Cayley graph and the coset geometry of von Dyck groups. G. Moreno, M. E. Stypa; Mathematica Slovaca 66 (2016).
  14. Completely exceptional 2nd order PDEs via conformal geometry and BGG resolution. J. Gutt, G. Manno, G. Moreno; Journal of Geometry and Physics (2016).
  15. Meta-Symplectic Geometry of 3rd Order Monge–Ampère Equations and their Characteristics. G. Manno, G. Moreno; SIGMA 12 (2016).
  16. Symplectic structures related with higher order variational problems. J. Kijowski, G. Moreno; International Journal of Geometric Methods in Modern Physics 12 (2015).
  17. Natural boundary conditions in geometric calculus of variations. G. Moreno, M. E. Stypa; Mathematica Slovaca 65 (2015).
  18. On a bicomplex induced by the variational sequence. D. Krupka, G. Moreno, Z. Urban, J. Volná; International Journal of Geometric Methods in Modern Physics 12 (2015).
  19. Remarks on non–maximal integral elements of the Cartan plane in jet spaces. M. Bächtold, G. Moreno; Journal of Geometry and Physics 85 (2014).
  20. The Geometry of the space of Cauchy data of nonlinear PDEs. G. Moreno; Central European Journal of Mathematics 11 (2013).
  21. The Bianchi variety. G. Moreno; Differential Geometry and its Applications 6 (2010).

Projects

Ochota na Naukę: działanie skierowane do uczniów gimnazjów i liceów, którzy chcą przeprowadzić własne badania naukowe. Program ,,Ochota na Naukę” jest finansowany przez Miasto Stołeczne Warszawa.

Complex contact manifolds and geometry of secants: the project is realized within the Sonata Bis (7th edition) programme of National Science Centre, Poland.

Dydaktyka

Matematyka I 2023/24