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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. The moment map on the space of symplectic 3D Monge-Ampère equations. Jan Gutt, Gianni Manno, Giovanni Moreno, Robert Śmiech; accepted by Advances in Differential Equations (2023).
  2. Third-order affine and projective-invariant (systems of) PDEs in two independent variables as vanishing of the Fubini-Pick invariant. Gianni Manno, Giovanni Moreno; preprint (2022).
  3. 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).
  4. Projectively and affinely invariant PDEs on hypersurfaces. Dmitri V. Alekseevsky, Jan Gutt, Gianni Manno, Giovanni Moreno; preprint (2019).
  5. Complex contact manifolds, varieties of minimal rational tangents, and exterior differential systems. Jarosław Buczyński, Giovanni Moreno; Banach Center Publications, 117 (2019) 145-176.
  6. Geometry of Lagrangian Grassmannians and Nonlinear PDEs. Jan Gutt, Gianni Manno, Giovanni Moreno; Banach Center Publications, 117 (2019) 9–44.
  7. 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.
  8. Contact manifolds, Lagrangian Grassmannians and PDEs. Olimjon Eshkobilov, Gianni Manno, Giovanni Moreno, Katja Sagerschnig; Complex Manifolds, 5 (2018) 26-88.
  9. An introduction to completely exceptional 2nd order scalar PDEs. Giovanni Moreno; Banach Centre Publications, 113 (2017) 275-289.
  10. On a geometric framework for Lagrangian Supermechanics. J. A. Bruce, K. Grabowska, G. Moreno; Journal of Geometric Mechanics 9(4), 411–437 (2017).
  11. Geometry of the free–sliding Bernoulli beam. G. Moreno, M. E. Stypa; Communications in Mathematics 24 (2016) 153–171.
  12. 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).
  13. Completely exceptional 2nd order PDEs via conformal geometry and BGG resolution. J. Gutt, G. Manno, G. Moreno; Journal of Geometry and Physics (2016).
  14. Meta-Symplectic Geometry of 3rd Order Monge–Ampère Equations and their Characteristics. G. Manno, G. Moreno; SIGMA 12 (2016).
  15. Symplectic structures related with higher order variational problems. J. Kijowski, G. Moreno; International Journal of Geometric Methods in Modern Physics 12 (2015).
  16. Natural boundary conditions in geometric calculus of variations. G. Moreno, M. E. Stypa; Mathematica Slovaca 65 (2015).
  17. 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).
  18. Remarks on non–maximal integral elements of the Cartan plane in jet spaces. M. Bächtold, G. Moreno; Journal of Geometry and Physics 85 (2014).
  19. The Geometry of the space of Cauchy data of nonlinear PDEs. G. Moreno; Central European Journal of Mathematics 11 (2013).
  20. 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 2022/23

Matematyka II 2023