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Marius Nicolae Crainic (February 3, 1973, Aiud ) is a Romanian mathematician working in the Netherlands .
Education and career
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Born in Aiud , Romania, Crainic obtained a bachelor's degree at Babeș-Bolyai University (Cluj-Napoca ) in 1995. He then moved to the Netherlands and obtained a master's degree in 1996 at Nijmegen University . He received his Ph.D. in 2000 from Utrecht University under the supervision of Ieke Moerdijk . His Ph.D. thesis is titled "Cyclic cohomology and characteristic classes for foliations ".[1]
He was a Miller Research Fellow [2] at the University of California, Berkeley from 2001 to 2002. He then returned to Utrecht University as a Fellow of the Royal Netherlands Academy of Arts and Sciences (KNAW). In 2007 he became an associate professor at Utrecht University, and since 2012 he is a full professor. In 2016 he was elected member of KNAW.[3]
In 2008 Crainic was awarded the André Lichnerowicz Prize in Poisson Geometry [4] [5] and in 2016 he received the De Bruijn Prize.[6] [7] In July 2020 he was an invited speaker to the 8th European congress of Mathematics ,[8] which has been rescheduled to 2021 due to the COVID-19 pandemic .[9]
Research
[ edit ]
Crainic's research interests lie in the field of differential geometry and its interactions with topology . His specialty is Poisson geometry [10] [11] [12] [13] [14] [15] and modern aspects of Lie theory , with several contributions to foliation theory ,[16] [17] symplectic geometry ,[18] Lie groupoids ,[19] [20] [21] [22] non-commutative geometry ,[23] Lie pseudogroups [24] and the geometry of PDEs .[25]
Among his most well-known results are a solution to the long-standing problem of describing the obstructions to the integrability of Lie algebroids[26] and a new geometric proof of Conn's linearization theorem,[27] both written in collaboration with Rui Loja Fernandes , as well as the development of the theory of representations up to homotopy .[28] [29]
He is the author of more than 30 research papers in peer-reviewed journals[30] and has supervised 10 PhD students as of 2020.[1]
References
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^ "Miller Institute News" (PDF) . Retrieved 2020-02-02 .
^ "Crainic, Prof. dr. M.N. (Marius) — KNAW" . www.knaw.nl . Archived from the original on 2020-05-17.
^ "Poisson Geometry Home Page" . www.lpthe.jussieu.fr . Retrieved 2020-01-30 .
^ "The André Lichneriwicz prize to Henrique Bursztyn and Marius Crainic" . euro-math-soc.eu . Retrieved 2020-02-01 .
^ "Mathematician Prof. Marius Crainic receives first De Bruijn Prize" . Utrecht University . 2017-09-21. Retrieved 2020-01-30 .
^ "Laudation for Marius Crainic" (PDF) . Retrieved 2020-02-02 .
^ "8th European Congress of Mathematics" . 8th European Congress of Mathematics . Retrieved 2020-02-01 .
^ "8th European Congress of Mathematics – 2020 rescheduled to June 2021" . 8th European Congress of Mathematics . Retrieved 2020-10-12 .
^ Crainic, Marius; Fernandes, Rui Loja (2004). "Integrability of Poisson Brackets" . J. Differential Geom . 66 (1 ): 71–137. arXiv :math/0210152 . doi :10.4310/jdg/1090415030 .
^ Crainic, Marius; Mǎrcuţ, Ioan (2012). "A normal form theorem around symplectic leaves" . J. Differential Geom . 92 (3 ): 417–461. arXiv :1009.2090 . doi :10.4310/jdg/1354110196 .
^ Crainic, Marius; Fernandes, Rui Loja; Martinez Torres, David (2019). "Poisson manifolds of compact types (PMCT 1)". Journal für die reine und angewandte Mathematik . 2019 (756): 101–149. arXiv :1510.07108 . doi :10.1515/crelle-2017-0006 . S2CID 7668127 .
^ Crainic, Marius; Mǎrcuţ, Ioan (2011). "On the existence of symplectic realizations" . Journal of Symplectic Geometry . 9 (2011) (4 ): 435–444. doi :10.4310/JSG.2011.v9.n4.a2 .
^ Crainic, Marius; Mǎrcuţ, Ioan (2015). "Reeb-Thurston stability for symplectic foliations" . Mathematische Annalen . 363 (1–2): 217–235. arXiv :1307.4363 . doi :10.1007/s00208-014-1167-7 .
^ Crainic, Marius; Fernandes, Rui Loja (2010). "Stability of symplectic leaves" . Inventiones Mathematicae . 180 (3 ): 481–533. arXiv :0810.4437 . Bibcode :2010InMat.180..481C . doi :10.1007/s00222-010-0235-1 .
^ Crainic, Marius; Moerdijk, Ieke (2000). "A homology theory for étale groupoids". Journal für die reine und angewandte Mathematik . 2000 (521): 25–46. doi :10.1515/crll.2000.029 . hdl :1874/19249 . S2CID 2607481 .
^ Crainic, Marius; Moerdijk, Ieke (2004). "Čech-De Rham theory for leaf spaces of foliations" (PDF) . Mathematische Annalen . 328 (2004): 59–85. doi :10.1007/s00208-003-0473-2 . S2CID 119151176 .
^ Crainic, Marius (2004). "Prequantization and Lie brackets". Journal of Symplectic Geometry . 2 (2004) (4 ): 579–602. arXiv :math/0403269 . Bibcode :2004math......3269C . doi :10.4310/JSG.2004.v2.n4.a3 . S2CID 8898100 .
^ Crainic, Marius (2003). "Differentiable and algebroid cohomology, Van Est isomorphisms, and characteristic classes" . Commentarii Mathematici Helvetici . 78 (4 ): 681–721. arXiv :math/0008064 . doi :10.1007/s00014-001-0766-9 .
^ Crainic, Marius; Struchiner, Ivan (2013). "On the linearization theorem for proper Lie groupoids" . Annales Scientifiques de l'École Normale Supérieure . Série 4. 46 (5 ): 723–746. arXiv :1103.5245 . doi :10.24033/asens.2200 . S2CID 119177832 .
^ Crainic, Marius; Struchiner, Ivan; Salazar, Maria Amelia (2015). "Multiplicative forms and Spencer operators". Mathematische Zeitschrift . 279 (3–4): 939–979. arXiv :1210.2277 . doi :10.1007/s00209-014-1398-z . S2CID 119545548 .
^ Crainic, Marius; Mestre, João Nuno (2018). "Orbispaces as differentiable stratified spaces" . Letters in Mathematical Physics . 108 (3 ): 805–859. arXiv :1705.00466 . Bibcode :2018LMaPh.108..805C . doi :10.1007/s11005-017-1011-6 . PMC 5818699 . PMID 29497239 .
^ Crainic, Marius (2002). "Cyclic cohomology of Hopf algebras". Journal of Pure and Applied Algebra . 166 (1–2): 29–66. doi :10.1016/S0022-4049(01 )00007-X . hdl :1874/1465 .
^ Crainic, Marius; Yudilevich, Ori (2017). "Lie Pseudogroups à la Cartan". arXiv :1801.00370 [math.DG ].
^ Cattafi, Francesco; Crainic, Marius; Salazar, Maria Amelia (2020-10-06). "From PDEs to Pfaffian fibrations" . L'Enseignement Mathématique . 66 (1 ): 187–250. arXiv :1901.02084 . doi :10.4171/LEM/66-1/2-10 . ISSN 0013-8584 . S2CID 213534860 .
^ Crainic, Marius; Fernandes, Rui (2003-03-01). "Integrability of Lie brackets" . Annals of Mathematics . 157 (2 ): 575–620. arXiv :math/0105033 . doi :10.4007/annals.2003.157.575 . ISSN 0003-486X .
^ Crainic, Marius; Fernandes, Rui Loja (2011-03-01). "A geometric approach to Conn's linearization theorem" . Annals of Mathematics . 173 (2 ): 1121–1139. arXiv :0812.3060 . doi :10.4007/annals.2011.173.2.14 . ISSN 0003-486X .
^ Crainic, Marius; Abad, Camilo Arias (2011-06-17). "Representations up to homotopy of Lie algebroids" (PDF) . Journal für die reine und angewandte Mathematik . 2012 (663): 91–126. doi :10.1515/CRELLE.2011.095 . ISSN 0075-4102 . S2CID 18662057 .
^ Crainic, Marius; Abad, Camilo Arias (2011). "The Weil algebra and the Van Est isomorphism" . Annales de l'Institut Fourier . 61 (2011) (3 ): 927–970. arXiv :0901.0322 . doi :10.5802/aif.2633 .
^ "Marius Crainic - Google Scholar Citations" . scholar.google.nl . Retrieved 2020-02-01 .
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