Janusz Grabowski

Janusz Roman Grabowski (born April 30, 1955 in Stalowa Wola, Poland) Polish mathematician working in differential geometry and mathematical methods in classical and quantum physics.

Biography

Janusz Roman Grabowski
Born 30th April 1955
Stalowa Wola
Occupation mathematician
Website https://www.impan.pl/~jagrab/

Scientific career

Grabowski earned his MSc degree in mathematics in 1978 at the Faculty of Mathematics, Informatics and Mechanics of the University of Warsaw. His master thesis was awarded the prize of Polish Mathematical Society. In the period of 1978-2001 he worked at the University of Warsaw earning his PhD in 1982 and habilitation in 1993. From 2001 he works in Institute of Mathematics Polish Academy of Sciences as a full professor. In 1988 and 1989 he was a fellow of Alexander von Humboldt Foundation. After political changes in Eastern Europe in 1989 he started an intensive international collaboration. He worked as visiting professor in many European scientific institutions, e.g. Erwin Schroedinger Institute in Vienna, University of Naples, University of Luxembourg and several Spanish universities. He acted also as an expert, panel member and panel chief in European Research Council. He supervised four PhD students.[1][2]

Scientific activity

The main idea of research activities of Janusz Grabowski is that one should try to find ‘the correct' framework, in which the considered problem really simplifies. Main results of his work include:

  1. Showing that k-tuple vector bundles can be characterized as manifolds equipped with k vector bundle structures with commuting Euler vector fields.[3][4]
  2. Introducing the concept of a graded bundle as a manifold with homogeneity structure, i.e. an action of multiplicative monoid of reals, together with its linearization.[5][6][7]
  3. Defining general algebroid and Tulczyjew triple related to it. This concept was then used in analytical mechanics to describe systems with symmetries and constraints, possibly nonholonomic.[8][9][10]
  4. Introducing the concept of Jacobi algebroid and Jacobi-Courant algebroid. In this approach Jacobi geometry is treated as homogeneous Poisson geometry.[11][12]
  5. Results on isomorphisms of Lie algebras of vector fields.[13]
  6. Geometrical approach to Lie systems of differential equations, i.e. systems of differential equations admitting a possibly nonlinear composition rule of solutions.[14]
  7. Poison-Nijenhuis structures on Lie algebroids.[15]
  8. Introducing the concept of a -supermanifold and results about its structure.[16]
  9. Geometric approach to problems in quantum informatics and entanglement.[17][18]

See also

References

  1. ↑ "Bazy danych - Nauka Polska". nauka-polska.pl. Retrieved 2016-11-17.
  2. ↑ "Janusz Grabowski - The Mathematics Genealogy Project". genealogy.math.ndsu.nodak.edu. Retrieved 2016-11-17.
  3. ↑ Grabowski, Janusz; Rotkiewicz, Mikołaj (2012-01-01). "Graded bundles and homogeneity structures". Journal of Geometry and Physics. 62 (1): 21–36. doi:10.1016/j.geomphys.2011.09.004.
  4. ↑ Grabowski, Janusz; Rotkiewicz, Mikołaj (2009-09-01). "Higher vector bundles and multi-graded symplectic manifolds". Journal of Geometry and Physics. 59 (9): 1285–1305. doi:10.1016/j.geomphys.2009.06.009.
  5. ↑ Bruce, Andrew James; Grabowska, Katarzyna; Grabowski, Janusz (2016-03-01). "Linear duals of graded bundles and higher analogues of (Lie) algebroids". Journal of Geometry and Physics. 101: 71–99. doi:10.1016/j.geomphys.2015.12.004.
  6. ↑ Bruce, Andrew James; Grabowska, Katarzyna; Grabowski, Janusz. "Graded Bundles in the Category of Lie Groupoids". Symmetry, Integrability and Geometry: Methods and Applications. 11. doi:10.3842/sigma.2015.090.
  7. ↑ Bruce, Andrew James; Grabowska, Katarzyna; Grabowski, Janusz. "Higher order mechanics on graded bundles". Journal of Physics A: Mathematical and Theoretical. 48 (20). doi:10.1088/1751-8113/48/20/205203.
  8. ↑ Grabowska, Katarzyna; Urbański, Paweł; Grabowski, Janusz (2006-05-01). "Geometrical mechanics on algebroids". International Journal of Geometric Methods in Modern Physics. 03 (03): 559–575. doi:10.1142/S0219887806001259. ISSN 0219-8878.
  9. ↑ Grabowska, Katarzyna; Grabowski, Janusz. "Variational calculus with constraints on general algebroids". Journal of Physics A: Mathematical and Theoretical. 41 (17). doi:10.1088/1751-8113/41/17/175204.
  10. ↑ Grabowski, J.; Urbański, P. (1999-09-01). "Algebroids — general differential calculi on vector bundles". Journal of Geometry and Physics. 31 (2): 111–141. doi:10.1016/S0393-0440(99)00007-8.
  11. ↑ Grabowski, Janusz; Marmo, Giuseppe (2001-01-01). "Jacobi structures revisited". Journal of Physics A: Mathematical and General. 34 (49): 10975. doi:10.1088/0305-4470/34/49/316. ISSN 0305-4470.
  12. ↑ Grabowski, Janusz (2013-06-01). "Graded contact manifolds and contact Courant algebroids". Journal of Geometry and Physics. 68: 27–58. doi:10.1016/j.geomphys.2013.02.001.
  13. ↑ Grabowski, J. (1978-03-22). "Isomorphisms and ideals of the Lie algebras of vector fields". Inventiones mathematicae. 50 (1): 13–33. doi:10.1007/BF01406466. ISSN 0020-9910. Retrieved 30 November 2016.
  14. ↑ Cariñena, J. F.; Grabowski, J.; Marmo, G. (2000). Lie-Scheffers Systems: A Geometric Approach. Napoli series on physics and astrophysics. 3. Bibliopolis. ISBN 9788870883787.
  15. ↑ Grabowski, Janusz; Urbański, Paweł (October 1997). "Lie algebroids and Poisson-Nijenhuis structures". Reports on Mathematical Physics. 40 (2): 195–208. doi:10.1016/S0034-4877(97)85916-2.
  16. ↑ Covolo, Tiffany; Grabowski, Janusz; Poncin, Norbert (2016-07-01). "The category of Z2n-supermanifolds". Journal of Mathematical Physics. 57 (7): 073503. doi:10.1063/1.4955416. ISSN 0022-2488.
  17. ↑ Grabowski, Janusz; Kuś, Marek; Marmo, Giuseppe. "Segre maps and entanglement for multipartite systems of indistinguishable particles". Journal of Physics A: Mathematical and Theoretical. 45 (10). doi:10.1088/1751-8113/45/10/105301.
  18. ↑ Grabowski, Janusz; Ibort, Alberto; Kuś, Marek; Marmo, Giuseppe. "Convex bodies of states and maps". Journal of Physics A: Mathematical and Theoretical. 46 (42). doi:10.1088/1751-8113/46/42/425301.

External links

This article is issued from Wikipedia - version of the 12/2/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.