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Marius Crainic

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Marius Crainic
Crainic in 2007
Born (1973-02-03) February 3, 1973 (age 51)
Aiud, Romania
NationalityRomanian
Alma materBabeș-Bolyai University
Utrecht University
AwardsAndré Lichnerowicz Prize, 2008
De Bruijn prize, 2016
Scientific career
FieldsMathematics
InstitutionsUtrecht University
Thesis Cyclic cohomology and characteristic classes for foliations  (2000)
Doctoral advisorIeke Moerdijk
Websitewebspace.science.uu.nl/~crain101/

Marius Nicolae Crainic (February 3, 1973, Aiud) is a Romanian mathematician working in the Netherlands.

Education and career

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

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

  1. ^ a b Marius Crainic at the Mathematics Genealogy Project
  2. ^ "Miller Institute News" (PDF). Retrieved 2020-02-02.
  3. ^ "Crainic, Prof. dr. M.N. (Marius) — KNAW". www.knaw.nl. Archived from the original on 2020-05-17.
  4. ^ "Poisson Geometry Home Page". www.lpthe.jussieu.fr. Retrieved 2020-01-30.
  5. ^ "The André Lichneriwicz prize to Henrique Bursztyn and Marius Crainic". euro-math-soc.eu. Retrieved 2020-02-01.
  6. ^ "Mathematician Prof. Marius Crainic receives first De Bruijn Prize". Utrecht University. 2017-09-21. Retrieved 2020-01-30.
  7. ^ "Laudation for Marius Crainic" (PDF). Retrieved 2020-02-02.
  8. ^ "8th European Congress of Mathematics". 8th European Congress of Mathematics. Retrieved 2020-02-01.
  9. ^ "8th European Congress of Mathematics – 2020 rescheduled to June 2021". 8th European Congress of Mathematics. Retrieved 2020-10-12.
  10. ^ Crainic, Marius; Fernandes, Rui Loja (2004). "Integrability of Poisson Brackets". J. Differential Geom. 66 (1): 71–137. doi:10.4310/jdg/1090415030.
  11. ^ Crainic, Marius; Mǎrcuţ, Ioan (2012). "A normal form theorem around symplectic leaves". J. Differential Geom. 92 (3): 417–461. doi:10.4310/jdg/1354110196.
  12. ^ 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.
  13. ^ 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.
  14. ^ Crainic, Marius; Mǎrcuţ, Ioan (2015). "Reeb-Thurston stability for symplectic foliations". Mathematische Annalen. 363 (1–2): 217–235. doi:10.1007/s00208-014-1167-7.
  15. ^ Crainic, Marius; Fernandes, Rui Loja (2010). "Stability of symplectic leaves". Inventiones Mathematicae. 180 (3): 481–533. Bibcode:2010InMat.180..481C. doi:10.1007/s00222-010-0235-1.
  16. ^ 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.
  17. ^ Crainic, Marius; Moerdijk, Ieke (2004). "Čech-De Rham theory for leaf spaces of foliations". Mathematische Annalen. 328 (2004): 59–85. doi:10.1007/s00208-003-0473-2. S2CID 119151176.
  18. ^ 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.
  19. ^ Crainic, Marius (2003). "Differentiable and algebroid cohomology, Van Est isomorphisms, and characteristic classes". Commentarii Mathematici Helvetici. 78 (4): 681–721. doi:10.1007/s00014-001-0766-9.
  20. ^ 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.
  21. ^ Crainic, Marius; Struchiner, Ivan; Salazar, Maria Amelia (2015). "Multiplicative forms and Spencer operators". Mathematische Zeitschrift. 279 (3–4): 939–979. doi:10.1007/s00209-014-1398-z. S2CID 119545548.
  22. ^ 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.
  23. ^ 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.
  24. ^ Crainic, Marius; Yudilevich, Ori (2017). "Lie Pseudogroups à la Cartan". arXiv:1801.00370 [math.DG].
  25. ^ 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.
  26. ^ Crainic, Marius; Fernandes, Rui (2003-03-01). "Integrability of Lie brackets". Annals of Mathematics. 157 (2): 575–620. doi:10.4007/annals.2003.157.575. ISSN 0003-486X.
  27. ^ Crainic, Marius; Fernandes, Rui Loja (2011-03-01). "A geometric approach to Conn's linearization theorem". Annals of Mathematics. 173 (2): 1121–1139. doi:10.4007/annals.2011.173.2.14. ISSN 0003-486X.
  28. ^ 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.
  29. ^ Crainic, Marius; Abad, Camilo Arias (2011). "The Weil algebra and the Van Est isomorphism". Annales de l'Institut Fourier. 61 (2011) (3): 927–970. doi:10.5802/aif.2633.
  30. ^ "Marius Crainic - Google Scholar Citations". scholar.google.nl. Retrieved 2020-02-01.
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