Janusz Grabowski

{{short description|Polish mathematician}} {{Multiple issues| {{like resume|date=December 2016}} {{Technical|date=August 2020}} }} {{Use dmy dates|date=July 2019}} {{Infobox person |name = Janusz Roman Grabowski |image = Janusz Grabowski, matematyk.jpg |birth_date = 30 April 1955 |birth_place = Stalowa Wola |occupation = Mathematician |website = https://www.impan.pl/~jagrab/}}

'''Janusz Roman Grabowski'''<ref>{{Cite web |title=Janusz Grabowski - personal page |url=https://www.impan.pl/~jagrab/ |access-date=2023-07-22 |website=www.impan.pl}}</ref> (born April 30, 1955 in Stalowa Wola, Poland) is a Polish mathematician working in differential geometry and mathematical methods in classical and quantum physics.

== 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.<ref>{{Cite web|url=http://nauka-polska.pl/dhtml/raporty/ludzieNauki?rtype=opis&objectId=23906&lang=en|title=Bazy danych - Nauka Polska|website=nauka-polska.pl|access-date=2016-11-17}}</ref><ref>{{Cite web|url=https://genealogy.math.ndsu.nodak.edu/id.php?id=54160|title=Janusz Grabowski - The Mathematics Genealogy Project|website=genealogy.math.ndsu.nodak.edu|access-date=2016-11-17}}</ref>

=== 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:

# Important results concerning Lie algebras of vector fields on smooth manifolds;<ref>{{cite journal|author=J. Grabowski|date=1978-02-01|doi=10.1007/BF01406466|issn=1432-1297|journal=Inventiones Mathematicae|language=en|number=1|pages=13–33|title=Isomorphisms and ideals of the Lie algebras of vector fields|volume=50|bibcode=1978InMat..50...13G |s2cid=121707492 }}</ref><ref>{{cite journal|access-date=2023-07-22|author=Janusz Grabowski|date=1981|issn=1570-5846|journal=Compositio Mathematica|language=fr|number=2|pages=239–252|title=Derivations of the Lie algebras of analytic vector fields|url=http://www.numdam.org/item/?id=CM_1981__43_2_239_0|volume=43}}</ref><ref>{{cite journal|access-date=2023-07-22|author=C. J. Atkin, J. Grabowski|date=1990|issn=1570-5846|journal=Compositio Mathematica|language=fr|number=3|pages=315–349|title=Homomorphisms of the Lie algebras associated with a symplectic manifold|url=http://www.numdam.org/item/?id=CM_1990__76_3_315_0|volume=76}}</ref> # A novel approach to double (and higher) vector bundles which drastically simplifies the theory;<ref>{{cite journal|access-date=2016-11-18|author=Janusz Grabowski, Mikołaj Rotkiewicz|date=2012-01-01|doi=10.1016/j.geomphys.2011.09.004|edition=1|journal=Journal of Geometry and Physics|pages=21–36|title=Graded bundles and homogeneity structures|volume=62 |issue=1 |arxiv=1102.0180 |bibcode=2012JGP....62...21G |s2cid=119661582 |url=http://www.sciencedirect.com/science/article/pii/S0393044011002051}}</ref><ref>{{cite journal|access-date=2016-11-18|author=Janusz Grabowski, Mikołaj Rotkiewicz|date=2009-09-01|doi=10.1016/j.geomphys.2009.06.009|edition=9|journal=Journal of Geometry and Physics|pages=1285–1305|title=Higher vector bundles and multi-graded symplectic manifolds|volume=59 |issue=9 |arxiv=math/0702772 |bibcode=2009JGP....59.1285G |s2cid=18565501 |url=http://www.sciencedirect.com/science/article/pii/S0393044009001041}}</ref> # Introducing the concepts of ''graded bundle'' and ''homogeneity structure'' with applications;<ref>{{cite journal|author=Janusz Grabowski, Katarzyna Grabowska, Paweł Urbański|date=2014|doi=10.3934/jgm.2014.6.503|issn=1941-4897|journal=Journal of Geometric Mechanics|number=4|pages=503–526|title=Geometry of Lagrangian and Hamiltonian formalisms in the dynamics of strings|volume=6|s2cid=54846675 |arxiv=1401.6970}}</ref><ref>{{cite journal|access-date=2016-11-18|author=Andrew James Bruce, Katarzyna Grabowska, Janusz Grabowski|date=2016-03-01|doi=10.1016/j.geomphys.2015.12.004|edition=101|journal=Journal of Geometry and Physics|pages=71–99|title=Linear duals of graded bundles and higher analogues of (Lie) algebroids|volume=101 |arxiv=1409.0439 |bibcode=2016JGP...101...71B |s2cid=119297483 |url=http://www.sciencedirect.com/science/article/pii/S039304401500279X}}</ref><ref>{{cite journal|access-date=2016-11-18|author=Andrew James Bruce, Institute of Mathematics, Polish Academy of Sciences, Poland, Katarzyna Grabowska|date=2015-11-11|doi=10.3842/sigma.2015.090|edition=11|journal=Symmetry, Integrability and Geometry: Methods and Applications|language=en|title=Graded Bundles in the Category of Lie Groupoids|volume=11 |page=090 |arxiv=1502.06092 |bibcode=2015SIGMA..11..090B |s2cid=15437294 |url=http://www.emis.de/journals/SIGMA/2015/090/}}</ref><ref>{{cite journal|author=Andrew James Bruce, Katarzyna Grabowska, Janusz Grabowski|doi=10.1088/1751-8113/48/20/205203|edition=20|journal=Journal of Physics A: Mathematical and Theoretical|title=Higher order mechanics on graded bundles|date=2015 |volume=48 |issue=20 |article-number=205203 |arxiv=1412.2719 |bibcode=2015JPhA...48t5203B |s2cid=119597985 |url=http://stacks.iop.org/1751-8121/48/i=20/a=205203?key=crossref.d61fe85cee807625e633b5d5d4dea5fe}}</ref><ref>{{cite journal|author=Katarzyna Grabowska, Janusz Grabowski, Zohreh Ravanpak|date=2022-07-01|doi=10.1007/s10455-022-09847-z|issn=1572-9060|journal=Annals of Global Analysis and Geometry|language=en|number=1|pages=235–284|title=VB-structures and generalizations|volume=62|arxiv=2108.06387 |s2cid=254189899 }}</ref> # Defining the concept of ''general algebroid'' and the corresponding Lagrangian and Hamiltonian formalisms, including nonholonomic constraints;<ref>{{cite journal|author=Katarzyna Grabowska, Janusz Grabowski|date=2013|doi=10.3934/jgm.2013.5.445|issn=1941-4897|journal=Journal of Geometric Mechanics|number=4|pages=445–472|title=Tulczyjew triples: From statics to field theory|volume=5|arxiv=1306.2744 |s2cid=119133193 }}</ref><ref>{{cite journal|access-date=2016-11-18|author=Katarzyna Grabowska, Paweł Urbański, Janusz Grabowski|date=2006-05-01|doi=10.1142/S0219887806001259|edition=03|issn=0219-8878|journal=International Journal of Geometric Methods in Modern Physics|pages=559–575|title=Geometrical mechanics on algebroids|volume=03 |issue=3 |url=http://www.worldscientific.com/doi/abs/10.1142/S0219887806001259|arxiv=math-ph/0509063}}</ref><ref>{{cite journal|author=Katarzyna Grabowska, Janusz Grabowski|doi=10.1088/1751-8113/41/17/175204|edition=17|journal=Journal of Physics A: Mathematical and Theoretical|title=Variational calculus with constraints on general algebroids|date=2008 |volume=41 |issue=17 |article-number=175204 |arxiv=0712.2766 |bibcode=2008JPhA...41q5204G |s2cid=115168368 |url=http://stacks.iop.org/1751-8121/41/i=17/a=175204?key=crossref.288d9dfbf1a18df3ded12312c69d6adb}}</ref><ref>{{cite journal|access-date=2016-11-18|author=J. Grabowski, P. Urbański|date=1999-09-01|doi=10.1016/S0393-0440(99)00007-8|edition=2|journal=Journal of Geometry and Physics|pages=111–141|title=Algebroids – general differential calculi on vector bundles|volume=31 |issue=2–3 |arxiv=math/9909174 |bibcode=1999JGP....31..111G |s2cid=119605066 |url=http://www.sciencedirect.com/science/article/pii/S0393044099000078}}</ref> # Results in the theory of Lie systems of differential equations;<ref>{{Cite journal |last1=Cariñena |first1=José F. |last2=Grabowski |first2=Janusz |last3=Ramos |first3=Arturo |date=2001-03-01 |title=Reduction of Time-Dependent Systems Admitting a Superposition Principle |journal=Acta Applicandae Mathematicae |language=en |volume=66 |issue=1 |pages=67–87 |doi=10.1023/A:1010743114995 |s2cid=118231737 |issn=1572-9036}}</ref><ref>{{Cite book|author=J. F. Cariñena|author2=J. Grabowski|author3=G. Marmo|title=Lie-Scheffers Systems: A Geometric Approach|date=2000|isbn=978-88-7088-378-7|chapter=Napoli series on physics and astrophysics|volume=3|publisher=Bibliopolis}}</ref><ref>{{Cite journal |last1=Cariñena |first1=José F. |last2=Grabowski |first2=Janusz |last3=Marmo |first3=Giuseppe |date=2007-10-01 |title=Superposition rules, lie theorem, and partial differential equations |url=https://www.sciencedirect.com/science/article/pii/S0034487707801376 |journal=Reports on Mathematical Physics |language=en |volume=60 |issue=2 |pages=237–258 |doi=10.1016/S0034-4877(07)80137-6 |arxiv=math-ph/0610013 |bibcode=2007RpMP...60..237C |s2cid=119561391 |issn=0034-4877}}</ref><ref>{{Cite journal |last1=Grabowski |first1=Janusz |last2=de Lucas |first2=Javier |date=2013-01-01 |title=Mixed superposition rules and the Riccati hierarchy |url=https://www.sciencedirect.com/science/article/pii/S0022039612003348 |journal=Journal of Differential Equations |language=en |volume=254 |issue=1 |pages=179–198 |doi=10.1016/j.jde.2012.08.020 |arxiv=1203.0123 |bibcode=2013JDE...254..179G |s2cid=119118704 |issn=0022-0396}}</ref> # Vital achievements in the theory of Poisson and Jacobi structures;<ref>{{cite journal|access-date=2023-07-22|author=Janusz Grabowski, Giuseppe Marmo|date=2002-12-12|doi=10.1088/0305-4470/36/1/311|issn=0305-4470|journal=Journal of Physics A: Mathematical and General|number=1|pages=161–181|title=The graded Jacobi algebras and (co)homology|url=https://iopscience.iop.org/article/10.1088/0305-4470/36/1/311|volume=36|arxiv=math/0207017 |s2cid=119143546 }}</ref><ref>{{cite journal|access-date=2023-07-22|author=Janusz Grabowski, Giuseppe Marmo|date=2001-12-05|doi=10.1088/0305-4470/34/49/316|issn=0305-4470|journal=Journal of Physics A: Mathematical and General|number=49|pages=10975–10990|title=Jacobi structures revisited|url=https://iopscience.iop.org/article/10.1088/0305-4470/34/49/316|volume=34|arxiv=math/0111148 |bibcode=2001JPhA...3410975G |s2cid=119644919 }}</ref><ref>{{cite journal|author=Janusz Grabowski|date=2012-12-01|doi=10.1007/s00031-012-9197-2|issn=1531-586X|journal=Transformation Groups|language=en|number=4|pages=989–1010|title=Modular classes of skew algebroid relations|volume=17|arxiv=1108.2366 |s2cid=253634861 }}</ref><ref>{{cite journal|access-date=2016-11-18|author=Janusz Grabowski, Paweł Urbański|date=1997-10-01|doi=10.1016/S0034-4877(97)85916-2|edition=2|journal=Reports on Mathematical Physics|pages=195–208|title=Lie algebroids and Poisson-Nijenhuis structures|volume=40 |issue=2 |arxiv=dg-ga/9710007 |bibcode=1997RpMP...40..195G |s2cid=16924893 |url=http://www.sciencedirect.com/science/article/pii/S0034487797859162}}</ref><ref>{{cite journal|access-date=2023-07-22|author=J Grabowski, P Urbanski|date=1995-12-07|doi=10.1088/0305-4470/28/23/024|issn=0305-4470|journal=Journal of Physics A: Mathematical and General|number=23|pages=6743–6777|title=Tangent lifts of Poisson and related structures|url=https://iopscience.iop.org/article/10.1088/0305-4470/28/23/024|volume=28|arxiv=math/0701076 |bibcode=1995JPhA...28.6743G |s2cid=16783224 }}</ref><ref>{{cite journal|access-date=2023-07-22|author=D. Alekseevsky, J. Grabowski, G. Marmo, P. W. Michor|date=1998-07-01|doi=10.1016/S0393-0440(97)00063-6|issn=0393-0440|journal=Journal of Geometry and Physics|language=en|number=3|pages=340–379|title=Poisson structures on double Lie groups|url=https://www.sciencedirect.com/science/article/pii/S0393044097000636|volume=26|arxiv=math/9801028 |bibcode=1998JGP....26..340A |s2cid=8394430 }}</ref><ref>{{cite journal|access-date=2023-07-22|author=J. Grabowski, N. Poncin|date=March 2004|doi=10.1112/S0010437X0300006X|issn=1570-5846|journal=Compositio Mathematica|language=en|number=2|pages=511–527|title=Automorphisms of quantum and classical Poisson algebras|url=https://www.cambridge.org/core/journals/compositio-mathematica/article/automorphisms-of-quantum-and-classical-poisson-algebras/EB864D5705B6D42CB7DD61F0483578D2|volume=140|s2cid=89609959 |arxiv=math/0211175}}</ref> # Geometry of quantum systems;<ref>{{cite journal|access-date=2023-07-22|author=Janusz Grabowski, Marek Kuś, Giuseppe Marmo|date=2005-12-25|doi=10.1088/0305-4470/38/47/011|issn=0305-4470|journal=Journal of Physics A: Mathematical and General|number=47|pages=10217–10244|title=Geometry of quantum systems: density states and entanglement|url=https://iopscience.iop.org/article/10.1088/0305-4470/38/47/011|volume=38|arxiv=math-ph/0507045 |bibcode=2005JPhA...3810217G |s2cid=13985828 }}</ref><ref>{{cite journal|access-date=2023-07-22|author=Janusz Grabowski, Marek Kuś, Giuseppe Marmo|date=December 2006|doi=10.1007/s11080-006-9013-3|issn=1230-1612|journal=Open Systems & Information Dynamics|number=4|pages=343–362|title=Symmetries, Group Actions, and Entanglement|url=https://www.worldscientific.com/doi/abs/10.1007/s11080-006-9013-3|volume=13|arxiv=math-ph/0603048 |s2cid=15774540 }}</ref> # Introducing the concept of <math>\mathbb{Z}_2^n</math>-supermanifold and proving fundamental results about their structure;<ref>{{cite journal|access-date=2016-11-18|author=Tiffany Covolo, Janusz Grabowski, Norbert Poncin|date=2016-07-01|doi=10.1063/1.4955416|edition=7|issn=0022-2488|journal=Journal of Mathematical Physics|article-number=073503|title=The category of Z2n-supermanifolds|volume=57 |issue=7 |arxiv=1602.03312 |bibcode=2016JMP....57g3503C |s2cid=119169052 |url=https://aip.scitation.org/doi/full/10.1063/1.4955416}}</ref><ref>{{cite journal|access-date=2023-07-22|author=Tiffany Covolo, Janusz Grabowski, Norbert Poncin|date=2016-12-01|doi=10.1016/j.geomphys.2016.09.006|issn=0393-0440|journal=Journal of Geometry and Physics|language=en|pages=393–401|title=Splitting theorem for Z2n-supermanifolds|url=https://www.sciencedirect.com/science/article/pii/S0393044016302261|volume=110|arxiv=1602.03671 |bibcode=2016JGP...110..393C |s2cid=119298863 }}</ref> # Results in information geometry and applying geometric methods to studying the theory of quantum information and entanglement;<ref>{{cite journal|author=Janusz Grabowski, Marek Kuś, Giuseppe Marmo|doi=10.1088/1751-8113/45/10/105301|edition=10|journal=Journal of Physics A: Mathematical and Theoretical|title=Segre maps and entanglement for multipartite systems of indistinguishable particles|date=2012 |volume=45 |issue=10 |article-number=105301 |arxiv=1111.4812 |bibcode=2012JPhA...45j5301G |s2cid=119166651 |url=http://stacks.iop.org/1751-8121/45/i=10/a=105301?key=crossref.886d5d2a3267e3fc31115dcdbe968cea}}</ref><ref>{{cite journal|author=Janusz Grabowski, Alberto Ibort, Marek Kuś, Giuseppe Marmo|doi=10.1088/1751-8113/46/42/425301|edition=42|journal=Journal of Physics A: Mathematical and Theoretical|title=Convex bodies of states and maps|date=2013 |volume=46 |issue=42 |article-number=425301 |arxiv=1306.3187 |bibcode=2013JPhA...46P5301G |s2cid=119695068 |url=http://stacks.iop.org/1751-8121/46/i=42/a=425301?key=crossref.65c7190d0f48d8718b49e0b33134c33d}}</ref><ref>{{cite journal|access-date=2023-07-22|author=Janusz Grabowski, Marek Kuś, Giuseppe Marmo|date=2011-03-31|doi=10.1088/1751-8113/44/17/175302|issn=1751-8113|journal=Journal of Physics A: Mathematical and Theoretical|number=17|article-number=175302|title=Entanglement for multipartite systems of indistinguishable particles|url=https://iopscience.iop.org/article/10.1088/1751-8113/44/17/175302|volume=44|arxiv=1012.0758 |bibcode=2011JPhA...44q5302G |s2cid=119131532 }}</ref><ref>{{cite journal|access-date=2023-07-22|author=Katarzyna Grabowska, Janusz Grabowski, Marek Kuś, Giuseppe Marmo|date=2019-11-18|doi=10.1088/1751-8121/ab542e|issn=1751-8113|journal=Journal of Physics A: Mathematical and Theoretical|number=50|page=505202|title=Lie groupoids in information geometry|url=https://iopscience.iop.org/article/10.1088/1751-8121/ab542e|volume=52|arxiv=1904.00709 |bibcode=2019JPhA...52X5202G |s2cid=90260079 }}</ref><ref>{{cite journal|access-date=2023-07-22|author=Katarzyna Grabowska, Janusz Grabowski, Marek Kuś, Giuseppe Marmo|date=March 2023|doi=10.1142/S0129055X22500428|issn=0129-055X|journal=Reviews in Mathematical Physics|number=2|title=Lifting statistical structures|url=https://www.worldscientific.com/doi/10.1142/S0129055X22500428|volume=35|pages=2250042–2250046 |article-number=2250042 |arxiv=2203.02938 |bibcode=2023RvMaP..3550042G |s2cid=248496016 }}</ref> # A novel approach to contact geometry with applications to analytical mechanics.<ref>{{cite journal|access-date=2023-07-22|author=Andrew James Bruce, Katarzyna Grabowska, Janusz Grabowski|date=2017-07-26|doi=10.3842/SIGMA.2017.059|journal=SIGMA. Symmetry, Integrability and Geometry: Methods and Applications|language=en|page=059|title=Remarks on Contact and Jacobi Geometry|url=http://www.emis.de/journals/SIGMA/2017/059/|volume=13|arxiv=1507.05405 |bibcode=2017SIGMA..13..059B |s2cid=37536782 }}</ref><ref>{{cite journal|access-date=2023-07-22|author=Janusz Grabowski|date=2013-06-01|doi=10.1016/j.geomphys.2013.02.001|issn=0393-0440|journal=Journal of Geometry and Physics|language=en|pages=27–58|title=Graded contact manifolds and contact Courant algebroids|url=https://www.sciencedirect.com/science/article/pii/S039304401300017X|volume=68|arxiv=1112.0759 |bibcode=2013JGP....68...27G |s2cid=119130668 }}</ref><ref>{{cite journal|access-date=2023-07-22|author=Katarzyna Grabowska, Janusz Grabowski|date=2022-10-28|doi=10.1088/1751-8121/ac9adb|issn=1751-8113|journal=Journal of Physics A: Mathematical and Theoretical|number=43|page=435204|title=A geometric approach to contact Hamiltonians and contact Hamilton–Jacobi theory|url=https://iopscience.iop.org/article/10.1088/1751-8121/ac9adb|volume=55|arxiv=2207.04484 |bibcode=2022JPhA...55Q5204G |s2cid=252977031 }}</ref><ref>{{cite journal|author=Katarzyna Grabowska, Janusz Grabowski|date=2023-06-02|doi=10.1007/s10231-023-01341-y|issn=1618-1891|journal=Annali di Matematica Pura ed Applicata |language=en|title=Reductions: precontact versus presymplectic|volume=202 |issue=6 |pages=2803–2839 |s2cid=254096308 |arxiv=2211.16792}}</ref>

== References == {{reflist}} <references responsive="0" />

== External links == * [https://www.ams.org/mathscinet/MRAuthorID/204202] Janusz Grabowski in MathSciNet database * [https://www.impan.pl/~jagrab/] Webpage of Janusz Grabowski * [http://nauka-polska.pl/dhtml/raporty/ludzieNauki?rtype=opis&objectId=23906&lang=pl] Janusz Grabowski in Polska Bibliografia Naukowa database * [4] [https://arxiv.org/find/grp_math/1/au:+Grabowski_Janusz/0/1/0/all/0/1?per_page=100 Janusz] Grabowski publications in arxiv database

{{DEFAULTSORT:Grabowski, Janusz}} Category:1955 births Category:Living people Category:20th-century Polish mathematicians Category:21st-century Polish mathematicians

Janusz Grabowski

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