Janusz Grabowski

Last updated

Janusz Roman Grabowski
Janusz Grabowski, matematyk.jpg
Born30 April 1955
Stalowa Wola
Occupation Mathematician
Website https://www.impan.pl/~jagrab/

Janusz Roman Grabowski [1] (born April 30, 1955 in Stalowa Wola, Poland) is a Polish mathematician working in differential geometry and mathematical methods in classical and quantum physics.

Contents

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 first degree Marcinkowski Prize of the 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. He was giving courses in Calculus I, II, III, Functional Analysis, Lie algebras and Lie groups, Differential Geometry, etc.

Since 2001 he works in the Institute of Mathematics Polish Academy of Sciences as a full professor and the Head of the Department of Mathematical Physics and Differential Geometry. He is also a member of the Scientific Council of the Institute.

In 1988 and 1989 he was a fellow of the Alexander von Humboldt Foundation. After political changes in Eastern Europe in 1989 he started an intensive international collaboration. He was visiting professor in many European scientific institutions, e.g., the Erwin Schroedinger Institute in Vienna, the University of Naples, the University of Luxembourg, and several Spanish universities and . He acted also as an expert, panel member, and for several years as the chair of the mathematical panel evaluating grants of the European Research Council. He supervised four PhD students. [2] [3]

Scientific activity

Professor Janusz Grabowski is an author of over 140 publications in top and very good international scientific journals with about 2000 citations indexed in the bases of the Web of Knowledge. Main results of his work include:

  1. Important results concerning Lie algebras of vector fields on smooth manifolds; [4] [5] [6]
  2. A novel approach to double (and higher) vector bundles which drastically simplifies the theory; [7] [8]
  3. Introducing the concepts of graded bundle and homogeneity structure with applications; [9] [10] [11] [12] [13]
  4. Defining the concept of general algebroid and the corresponding Lagrangian and Hamiltonian formalisms, including nonholonomic constraints; [14] [15] [16] [17]
  5. Results in the theory of Lie systems of differential equations; [18] [19] [20] [21]
  6. Vital achievements in the theory of Poisson and Jacobi structures; [22] [23] [24] [25] [26] [27] [28]
  7. Geometry of quantum systems; [29] [30]
  8. Introducing the concept of -supermanifold and proving fundamental results about their structure; [31] [32]
  9. Results in information geometry and applying geometric methods to studying the theory of quantum information and entanglement; [33] [34] [35] [36] [37]
  10. A novel approach to contact geometry with applications to analytical mechanics. [38] [39] [40] [41]

Related Research Articles

In theoretical physics, twistor theory was proposed by Roger Penrose in 1967 as a possible path to quantum gravity and has evolved into a widely studied branch of theoretical and mathematical physics. Penrose's idea was that twistor space should be the basic arena for physics from which space-time itself should emerge. It has led to powerful mathematical tools that have applications to differential and integral geometry, nonlinear differential equations and representation theory, and in physics to general relativity, quantum field theory, and the theory of scattering amplitudes.

Objective-collapse theories, also known spontaneous collapse models or dynamical reduction models, are proposed solutions to the measurement problem in quantum mechanics. As with other interpretations of quantum mechanics, they are possible explanations of why and how quantum measurements always give definite outcomes, not a superposition of them as predicted by the Schrödinger equation, and more generally how the classical world emerges from quantum theory. The fundamental idea is that the unitary evolution of the wave function describing the state of a quantum system is approximate. It works well for microscopic systems, but progressively loses its validity when the mass / complexity of the system increases.

<span class="mw-page-title-main">Percolation threshold</span> Threshold of percolation theory models

The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in random systems. Below the threshold a giant connected component does not exist; while above it, there exists a giant component of the order of system size. In engineering and coffee making, percolation represents the flow of fluids through porous media, but in the mathematics and physics worlds it generally refers to simplified lattice models of random systems or networks (graphs), and the nature of the connectivity in them. The percolation threshold is the critical value of the occupation probability p, or more generally a critical surface for a group of parameters p1, p2, ..., such that infinite connectivity (percolation) first occurs.

The Fermi–Ulam model (FUM) is a dynamical system that was introduced by Polish mathematician Stanislaw Ulam in 1961.

In mathematics, in the area of quantum information geometry, the Bures metric or Helstrom metric defines an infinitesimal distance between density matrix operators defining quantum states. It is a quantum generalization of the Fisher information metric, and is identical to the Fubini–Study metric when restricted to the pure states alone.

<span class="mw-page-title-main">Vladimir Korepin</span> Russian physicist and mathematician

Vladimir E. Korepin is a professor at the C. N. Yang Institute of Theoretical Physics of the Stony Brook University. Korepin made research contributions in several areas of mathematics and physics.

In the context of the physical and mathematical theory of percolation, a percolation transition is characterized by a set of universal critical exponents, which describe the fractal properties of the percolating medium at large scales and sufficiently close to the transition. The exponents are universal in the sense that they only depend on the type of percolation model and on the space dimension. They are expected to not depend on microscopic details such as the lattice structure, or whether site or bond percolation is considered. This article deals with the critical exponents of random percolation.

The SP formula for the dephasing rate of a particle that moves in a fluctuating environment unifies various results that have been obtained, notably in condensed matter physics, with regard to the motion of electrons in a metal. The general case requires to take into account not only the temporal correlations but also the spatial correlations of the environmental fluctuations. These can be characterized by the spectral form factor , while the motion of the particle is characterized by its power spectrum . Consequently, at finite temperature the expression for the dephasing rate takes the following form that involves S and P functions:

<span class="mw-page-title-main">Matilde Marcolli</span> Italian mathematician and physicist

Matilde Marcolli is an Italian and American mathematical physicist. She has conducted research work in areas of mathematics and theoretical physics; obtained the Heinz Maier-Leibnitz-Preis of the Deutsche Forschungsgemeinschaft, and the Sofia Kovalevskaya Award of the Alexander von Humboldt Foundation. Marcolli has authored and edited numerous books in the field. She is currently the Robert F. Christy Professor of Mathematics and Computing and Mathematical Sciences at the California Institute of Technology.

<span class="mw-page-title-main">Maurice A. de Gosson</span> Austrian mathematician and mathematical physicist

Maurice A. de Gosson, is an Austrian mathematician and mathematical physicist, born in Berlin. He is currently a Senior Researcher at the Numerical Harmonic Analysis Group (NuHAG) of the University of Vienna.

In mathematical physics, the ternary commutator is an additional ternary operation on a triple system defined by

In potential theory, a branch of mathematics, the Laplacian of the indicator of the domain D is a generalisation of the derivative of the Dirac delta function to higher dimensions, and is non-zero only on the surface of D. It can be viewed as the surface delta prime function. It is analogous to the second derivative of the Heaviside step function in one dimension. It can be obtained by letting the Laplace operator work on the indicator function of some domain D.

Dynamic scaling is a litmus test that shows whether an evolving system exhibits self-similarity. In general a function is said to exhibit dynamic scaling if it satisfies:

Dorje C. Brody is a British applied mathematician and mathematical physicist.

Olaf Lechtenfeld is a German mathematical physicist, academic and researcher. He is a full professor at the Institute of Theoretical Physics at Leibniz University, where he founded the Riemann Center for Geometry and Physics.

Anatol Odzijewicz [ was Polish mathematician and physicist. The main areas of his research were the theory of Banach groupoids and algebroids related to the structure of W*-algebras, quantization of physical systems by means of the coherent state map, as well as quantum and classical integrable systems.

Robert Schrader was a German theoretical and mathematical physicist and professor of the Free University of Berlin. He is known for the Osterwalder–Schrader axioms.

Jorge Kurchan is an Argentine-Italian statistical physicist. He is currently Director of Exceptional Class Research at the French National Centre for Scientific Research (CNRS). His primary areas of study include statistical physics, non-equilibrium thermodynamics, and complex systems. Kurchans research often explores topics such as glassy dynamics, stochastic processes, and the behavior of disordered systems, focusing on understanding the fundamental principles underlying the statistical mechanics of complex and out-of-equilibrium systems.

References

  1. ↑ "Janusz Grabowski - personal page". www.impan.pl. Retrieved 22 July 2023.
  2. ↑ "Bazy danych - Nauka Polska". nauka-polska.pl. Retrieved 17 November 2016.
  3. ↑ "Janusz Grabowski - The Mathematics Genealogy Project". genealogy.math.ndsu.nodak.edu. Retrieved 17 November 2016.
  4. ↑ J. Grabowski (1 February 1978). "Isomorphisms and ideals of the Lie algebras of vector fields". Inventiones Mathematicae. 50 (1): 13–33. Bibcode:1978InMat..50...13G. doi:10.1007/BF01406466. ISSN   1432-1297. S2CID   121707492 . Retrieved 22 July 2023.
  5. ↑ Janusz Grabowski (1981). "Derivations of the Lie algebras of analytic vector fields". Compositio Mathematica (in French). 43 (2): 239–252. ISSN   1570-5846 . Retrieved 22 July 2023.
  6. ↑ C. J. Atkin, J. Grabowski (1990). "Homomorphisms of the Lie algebras associated with a symplectic manifold". Compositio Mathematica (in French). 76 (3): 315–349. ISSN   1570-5846 . Retrieved 22 July 2023.
  7. ↑ Janusz Grabowski, Mikołaj Rotkiewicz (1 January 2012). "Graded bundles and homogeneity structures". Journal of Geometry and Physics. 62 (1) (1 ed.): 21–36. arXiv: 1102.0180 . Bibcode:2012JGP....62...21G. doi:10.1016/j.geomphys.2011.09.004. S2CID   119661582 . Retrieved 18 November 2016.
  8. ↑ Janusz Grabowski, Mikołaj Rotkiewicz (1 September 2009). "Higher vector bundles and multi-graded symplectic manifolds". Journal of Geometry and Physics. 59 (9) (9 ed.): 1285–1305. arXiv: math/0702772 . Bibcode:2009JGP....59.1285G. doi:10.1016/j.geomphys.2009.06.009. S2CID   18565501 . Retrieved 18 November 2016.
  9. ↑ Janusz Grabowski, Katarzyna Grabowska, Paweł Urbański (2014). "Geometry of Lagrangian and Hamiltonian formalisms in the dynamics of strings". Journal of Geometric Mechanics. 6 (4): 503–526. arXiv: 1401.6970 . doi:10.3934/jgm.2014.6.503. ISSN   1941-4897. S2CID   54846675 . Retrieved 22 July 2023.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  10. ↑ Andrew James Bruce, Katarzyna Grabowska, Janusz Grabowski (1 March 2016). "Linear duals of graded bundles and higher analogues of (Lie) algebroids". Journal of Geometry and Physics. 101 (101 ed.): 71–99. arXiv: 1409.0439 . Bibcode:2016JGP...101...71B. doi:10.1016/j.geomphys.2015.12.004. S2CID   119297483 . Retrieved 18 November 2016.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  11. ↑ Andrew James Bruce, Institute of Mathematics, Polish Academy of Sciences, Poland, Katarzyna Grabowska (11 November 2015). "Graded Bundles in the Category of Lie Groupoids". Symmetry, Integrability and Geometry: Methods and Applications. 11 (11 ed.): 090. arXiv: 1502.06092 . Bibcode:2015SIGMA..11..090B. doi:10.3842/sigma.2015.090. S2CID   15437294 . Retrieved 18 November 2016.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  12. ↑ Andrew James Bruce, Katarzyna Grabowska, Janusz Grabowski (2015). "Higher order mechanics on graded bundles". Journal of Physics A: Mathematical and Theoretical. 48 (20) (20 ed.): 205203. arXiv: 1412.2719 . Bibcode:2015JPhA...48t5203B. doi:10.1088/1751-8113/48/20/205203. S2CID   119597985.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  13. ↑ Katarzyna Grabowska, Janusz Grabowski, Zohreh Ravanpak (1 July 2022). "VB-structures and generalizations". Annals of Global Analysis and Geometry. 62 (1): 235–284. arXiv: 2108.06387 . doi:10.1007/s10455-022-09847-z. ISSN   1572-9060. S2CID   254189899 . Retrieved 22 July 2023.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  14. ↑ Katarzyna Grabowska, Janusz Grabowski (2013). "Tulczyjew triples: From statics to field theory". Journal of Geometric Mechanics. 5 (4): 445–472. arXiv: 1306.2744 . doi:10.3934/jgm.2013.5.445. ISSN   1941-4897. S2CID   119133193 . Retrieved 22 July 2023.
  15. ↑ Katarzyna Grabowska, Paweł Urbański, Janusz Grabowski (1 May 2006). "Geometrical mechanics on algebroids". International Journal of Geometric Methods in Modern Physics. 03 (3) (03 ed.): 559–575. arXiv: math-ph/0509063 . doi:10.1142/S0219887806001259. ISSN   0219-8878 . Retrieved 18 November 2016.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  16. ↑ Katarzyna Grabowska, Janusz Grabowski (2008). "Variational calculus with constraints on general algebroids". Journal of Physics A: Mathematical and Theoretical. 41 (17) (17 ed.): 175204. arXiv: 0712.2766 . Bibcode:2008JPhA...41q5204G. doi:10.1088/1751-8113/41/17/175204. S2CID   115168368.
  17. ↑ J. Grabowski, P. Urbański (1 September 1999). "Algebroids – general differential calculi on vector bundles". Journal of Geometry and Physics. 31 (2–3) (2 ed.): 111–141. arXiv: math/9909174 . Bibcode:1999JGP....31..111G. doi:10.1016/S0393-0440(99)00007-8. S2CID   119605066 . Retrieved 18 November 2016.
  18. ↑ Cariñena, José F.; Grabowski, Janusz; Ramos, Arturo (1 March 2001). "Reduction of Time-Dependent Systems Admitting a Superposition Principle". Acta Applicandae Mathematicae. 66 (1): 67–87. doi:10.1023/A:1010743114995. ISSN   1572-9036. S2CID   118231737.
  19. ↑ J. F. Cariñena; J. Grabowski; G. Marmo (2000). "Napoli series on physics and astrophysics". Lie-Scheffers Systems: A Geometric Approach. Vol. 3. Bibliopolis. ISBN   9788870883787.
  20. ↑ Cariñena, José F.; Grabowski, Janusz; Marmo, Giuseppe (1 October 2007). "Superposition rules, lie theorem, and partial differential equations". Reports on Mathematical Physics. 60 (2): 237–258. arXiv: math-ph/0610013 . Bibcode:2007RpMP...60..237C. doi:10.1016/S0034-4877(07)80137-6. ISSN   0034-4877. S2CID   119561391.
  21. ↑ Grabowski, Janusz; de Lucas, Javier (1 January 2013). "Mixed superposition rules and the Riccati hierarchy". Journal of Differential Equations. 254 (1): 179–198. arXiv: 1203.0123 . Bibcode:2013JDE...254..179G. doi:10.1016/j.jde.2012.08.020. ISSN   0022-0396. S2CID   119118704.
  22. ↑ Janusz Grabowski, Giuseppe Marmo (12 December 2002). "The graded Jacobi algebras and (co)homology". Journal of Physics A: Mathematical and General. 36 (1): 161–181. arXiv: math/0207017 . doi:10.1088/0305-4470/36/1/311. ISSN   0305-4470. S2CID   119143546 . Retrieved 22 July 2023.
  23. ↑ Janusz Grabowski, Giuseppe Marmo (5 December 2001). "Jacobi structures revisited". Journal of Physics A: Mathematical and General. 34 (49): 10975–10990. arXiv: math/0111148 . Bibcode:2001JPhA...3410975G. doi:10.1088/0305-4470/34/49/316. ISSN   0305-4470. S2CID   119644919 . Retrieved 22 July 2023.
  24. ↑ Janusz Grabowski (1 December 2012). "Modular classes of skew algebroid relations". Transformation Groups. 17 (4): 989–1010. arXiv: 1108.2366 . doi:10.1007/s00031-012-9197-2. ISSN   1531-586X. S2CID   253634861 . Retrieved 22 July 2023.
  25. ↑ Janusz Grabowski, Paweł Urbański (1 October 1997). "Lie algebroids and Poisson-Nijenhuis structures". Reports on Mathematical Physics. 40 (2) (2 ed.): 195–208. arXiv: dg-ga/9710007 . Bibcode:1997RpMP...40..195G. doi:10.1016/S0034-4877(97)85916-2. S2CID   16924893 . Retrieved 18 November 2016.
  26. ↑ J Grabowski, P Urbanski (7 December 1995). "Tangent lifts of Poisson and related structures". Journal of Physics A: Mathematical and General. 28 (23): 6743–6777. arXiv: math/0701076 . Bibcode:1995JPhA...28.6743G. doi:10.1088/0305-4470/28/23/024. ISSN   0305-4470. S2CID   16783224 . Retrieved 22 July 2023.
  27. ↑ D. Alekseevsky, J. Grabowski, G. Marmo, P. W. Michor (1 July 1998). "Poisson structures on double Lie groups". Journal of Geometry and Physics. 26 (3): 340–379. arXiv: math/9801028 . Bibcode:1998JGP....26..340A. doi:10.1016/S0393-0440(97)00063-6. ISSN   0393-0440. S2CID   8394430 . Retrieved 22 July 2023.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  28. ↑ J. Grabowski, N. Poncin (March 2004). "Automorphisms of quantum and classical Poisson algebras". Compositio Mathematica. 140 (2): 511–527. arXiv: math/0211175 . doi:10.1112/S0010437X0300006X. ISSN   1570-5846. S2CID   89609959 . Retrieved 22 July 2023.
  29. ↑ Janusz Grabowski, Marek Kuś, Giuseppe Marmo (25 December 2005). "Geometry of quantum systems: density states and entanglement". Journal of Physics A: Mathematical and General. 38 (47): 10217–10244. arXiv: math-ph/0507045 . Bibcode:2005JPhA...3810217G. doi:10.1088/0305-4470/38/47/011. ISSN   0305-4470. S2CID   13985828 . Retrieved 22 July 2023.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  30. ↑ Janusz Grabowski, Marek Kuś, Giuseppe Marmo (December 2006). "Symmetries, Group Actions, and Entanglement". Open Systems & Information Dynamics. 13 (4): 343–362. arXiv: math-ph/0603048 . doi:10.1007/s11080-006-9013-3. ISSN   1230-1612. S2CID   15774540 . Retrieved 22 July 2023.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  31. ↑ Tiffany Covolo, Janusz Grabowski, Norbert Poncin (1 July 2016). "The category of Z2n-supermanifolds". Journal of Mathematical Physics. 57 (7) (7 ed.): 073503. arXiv: 1602.03312 . Bibcode:2016JMP....57g3503C. doi:10.1063/1.4955416. ISSN   0022-2488. S2CID   119169052 . Retrieved 18 November 2016.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  32. ↑ Tiffany Covolo, Janusz Grabowski, Norbert Poncin (1 December 2016). "Splitting theorem for Z2n-supermanifolds". Journal of Geometry and Physics. 110: 393–401. arXiv: 1602.03671 . Bibcode:2016JGP...110..393C. doi:10.1016/j.geomphys.2016.09.006. ISSN   0393-0440. S2CID   119298863 . Retrieved 22 July 2023.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  33. ↑ Janusz Grabowski, Marek Kuś, Giuseppe Marmo (2012). "Segre maps and entanglement for multipartite systems of indistinguishable particles". Journal of Physics A: Mathematical and Theoretical. 45 (10) (10 ed.): 105301. arXiv: 1111.4812 . Bibcode:2012JPhA...45j5301G. doi:10.1088/1751-8113/45/10/105301. S2CID   119166651.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  34. ↑ Janusz Grabowski, Alberto Ibort, Marek Kuś, Giuseppe Marmo (2013). "Convex bodies of states and maps". Journal of Physics A: Mathematical and Theoretical. 46 (42) (42 ed.): 425301. arXiv: 1306.3187 . Bibcode:2013JPhA...46P5301G. doi:10.1088/1751-8113/46/42/425301. S2CID   119695068.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  35. ↑ Janusz Grabowski, Marek Kuś, Giuseppe Marmo (31 March 2011). "Entanglement for multipartite systems of indistinguishable particles". Journal of Physics A: Mathematical and Theoretical. 44 (17): 175302. arXiv: 1012.0758 . Bibcode:2011JPhA...44q5302G. doi:10.1088/1751-8113/44/17/175302. ISSN   1751-8113. S2CID   119131532 . Retrieved 22 July 2023.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  36. ↑ Katarzyna Grabowska, Janusz Grabowski, Marek Kuś, Giuseppe Marmo (18 November 2019). "Lie groupoids in information geometry". Journal of Physics A: Mathematical and Theoretical. 52 (50): 505202. arXiv: 1904.00709 . Bibcode:2019JPhA...52X5202G. doi:10.1088/1751-8121/ab542e. ISSN   1751-8113. S2CID   90260079 . Retrieved 22 July 2023.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  37. ↑ Katarzyna Grabowska, Janusz Grabowski, Marek Kuś, Giuseppe Marmo (March 2023). "Lifting statistical structures". Reviews in Mathematical Physics. 35 (2): 2250042–2250046. arXiv: 2203.02938 . Bibcode:2023RvMaP..3550042G. doi:10.1142/S0129055X22500428. ISSN   0129-055X. S2CID   248496016 . Retrieved 22 July 2023.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  38. ↑ Andrew James Bruce, Katarzyna Grabowska, Janusz Grabowski (26 July 2017). "Remarks on Contact and Jacobi Geometry". SIGMA. Symmetry, Integrability and Geometry: Methods and Applications. 13: 059. arXiv: 1507.05405 . Bibcode:2017SIGMA..13..059B. doi:10.3842/SIGMA.2017.059. S2CID   37536782 . Retrieved 22 July 2023.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  39. ↑ Janusz Grabowski (1 June 2013). "Graded contact manifolds and contact Courant algebroids". Journal of Geometry and Physics. 68: 27–58. arXiv: 1112.0759 . Bibcode:2013JGP....68...27G. doi:10.1016/j.geomphys.2013.02.001. ISSN   0393-0440. S2CID   119130668 . Retrieved 22 July 2023.
  40. ↑ Katarzyna Grabowska, Janusz Grabowski (28 October 2022). "A geometric approach to contact Hamiltonians and contact Hamilton–Jacobi theory". Journal of Physics A: Mathematical and Theoretical. 55 (43): 435204. arXiv: 2207.04484 . Bibcode:2022JPhA...55Q5204G. doi:10.1088/1751-8121/ac9adb. ISSN   1751-8113. S2CID   252977031 . Retrieved 22 July 2023.
  41. ↑ Katarzyna Grabowska, Janusz Grabowski (2 June 2023). "Reductions: precontact versus presymplectic". Annali di Matematica Pura ed Applicata. 202 (6): 2803–2839. arXiv: 2211.16792 . doi:10.1007/s10231-023-01341-y. ISSN   1618-1891. S2CID   254096308 . Retrieved 22 July 2023.
    This page is based on this Wikipedia article
    Text is available under the CC BY-SA 4.0 license; additional terms may apply.
    Images, videos and audio are available under their respective licenses.