Marius Crainic Explained

Marius Crainic
Birth Date:3 February 1973
Birth Place:Aiud, Romania
Nationality:Romanian
Alma Mater:Babeș-Bolyai University
Utrecht University
Doctoral Advisor:Ieke Moerdijk
Fields:Mathematics
Thesis Title:Cyclic cohomology and characteristic classes for foliations
Thesis Year:2000
Workplaces:Utrecht University
Awards:André Lichnerowicz Prize, 2008
De Bruijn prize, 2016

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".

He was a Miller Research Fellow[1] 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.[2]

In 2008 Crainic was awarded the André Lichnerowicz Prize in Poisson Geometry[3] [4] and in 2016 he received the De Bruijn Prize.[5] [6] In July 2020 he was an invited speaker to the 8th European congress of Mathematics,[7] which has been rescheduled to 2021 due to the COVID-19 pandemic.[8]

Research

Crainic's research interests lie in the field of differential geometry and its interactions with topology. His specialty is Poisson geometry[9] [10] [11] [12] [13] [14] and modern aspects of Lie theory, with several contributions to foliation theory,[15] [16] symplectic geometry,[17] Lie groupoids,[18] [19] [20] [21] non-commutative geometry,[22] Lie pseudogroups[23] and the geometry of PDEs.[24]

Among his most well-known results are a solution to the long-standing problem of describing the obstructions to the integrability of Lie algebroids[25] and a new geometric proof of Conn's linearization theorem,[26] both written in collaboration with Rui Loja Fernandes, as well as the development of the theory of representations up to homotopy.[27] [28]

He is the author of more than 30 research papers in peer-reviewed journals[29] and has supervised 10 PhD students as of 2020.

References

  1. Web site: Miller Institute News . 2020-02-02.
  2. Web site: Crainic, Prof. dr. M.N. (Marius) — KNAW. https://web.archive.org/web/20200517164100/https://www.knaw.nl/en/members/members/12165. www.knaw.nl. 2020-05-17.
  3. Web site: Poisson Geometry Home Page. www.lpthe.jussieu.fr. 2020-01-30.
  4. Web site: The André Lichneriwicz prize to Henrique Bursztyn and Marius Crainic. euro-math-soc.eu. en. 2020-02-01.
  5. Web site: Mathematician Prof. Marius Crainic receives first De Bruijn Prize. 2017-09-21. Utrecht University. en. 2020-01-30.
  6. Web site: Laudation for Marius Crainic . 2020-02-02.
  7. Web site: 8th European Congress of Mathematics. 2020-02-01. 8th European Congress of Mathematics.
  8. Web site: 8th European Congress of Mathematics – 2020 rescheduled to June 2021. 2020-10-12. 8th European Congress of Mathematics.
  9. Crainic. Marius. Fernandes. Rui Loja. Integrability of Poisson Brackets. J. Differential Geom.. 66. 1. 71–137. 10.4310/jdg/1090415030. 2004. free. math/0210152.
  10. Crainic. Marius. Mǎrcuţ. Ioan. A normal form theorem around symplectic leaves. J. Differential Geom.. 92. 3. 417–461. 10.4310/jdg/1354110196. 2012. free. 1009.2090.
  11. Crainic. Marius. Fernandes. Rui Loja. Martinez Torres. David. Poisson manifolds of compact types (PMCT 1). Journal für die reine und angewandte Mathematik. 2019. 756. 101–149. 10.1515/crelle-2017-0006. 2019. 1510.07108. 7668127.
  12. Crainic. Marius. Mǎrcuţ. Ioan. On the existence of symplectic realizations. Journal of Symplectic Geometry. 9 (2011). 4. 435–444. 10.4310/JSG.2011.v9.n4.a2. 2011. free.
  13. Crainic. Marius. Mǎrcuţ. Ioan. Reeb-Thurston stability for symplectic foliations. Mathematische Annalen. 363. 1–2. 217–235. 10.1007/s00208-014-1167-7. 2015. free. 1307.4363.
  14. Crainic. Marius. Fernandes. Rui Loja. Stability of symplectic leaves. Inventiones Mathematicae. 180. 3. 481–533. 10.1007/s00222-010-0235-1. 2010. 2010InMat.180..481C. free. 0810.4437.
  15. Crainic. Marius. Moerdijk. Ieke. A homology theory for étale groupoids. Journal für die reine und angewandte Mathematik. 2000. 521. 25–46. 10.1515/crll.2000.029. 2000. 1874/19249. 2607481. free.
  16. Crainic. Marius. Moerdijk. Ieke. Čech-De Rham theory for leaf spaces of foliations. Mathematische Annalen. 328. 2004. 59–85. 10.1007/s00208-003-0473-2. 2004. 119151176.
  17. Crainic. Marius. Prequantization and Lie brackets. Journal of Symplectic Geometry. 2 (2004). 4. 579–602. 10.4310/JSG.2004.v2.n4.a3. 2004. 2004math......3269C. math/0403269. 8898100.
  18. Crainic. Marius. Differentiable and algebroid cohomology, Van Est isomorphisms, and characteristic classes. Commentarii Mathematici Helvetici. 78. 4. 681–721. 10.1007/s00014-001-0766-9. 2003. free. math/0008064.
  19. Crainic. Marius. Struchiner. Ivan. On the linearization theorem for proper Lie groupoids. Annales Scientifiques de l'École Normale Supérieure . Série 4. 46 . 5. 723–746. 10.24033/asens.2200. 2013. 1103.5245 . 119177832.
  20. Crainic. Marius. Struchiner. Ivan. Salazar. Maria Amelia. Multiplicative forms and Spencer operators. Mathematische Zeitschrift. 279. 3–4. 939–979. 10.1007/s00209-014-1398-z. 2015. 119545548. 1210.2277.
  21. Crainic. Marius. Mestre. João Nuno. Orbispaces as differentiable stratified spaces. Letters in Mathematical Physics. 108. 3. 805–859. 10.1007/s11005-017-1011-6. 2018. 29497239. 5818699. 2018LMaPh.108..805C. 1705.00466.
  22. Crainic. Marius. Cyclic cohomology of Hopf algebras. Journal of Pure and Applied Algebra. 166. 1–2. 29–66. 10.1016/S0022-4049(01)00007-X. 2002. 1874/1465. free.
  23. Crainic. Marius. Yudilevich. Ori. Lie Pseudogroups à la Cartan. 1801.00370. math.DG. 2017.
  24. Cattafi. Francesco. Crainic. Marius. Salazar. Maria Amelia. 2020-10-06. From PDEs to Pfaffian fibrations. L'Enseignement Mathématique. en. 66. 1. 187–250. 10.4171/LEM/66-1/2-10. 1901.02084. 213534860. 0013-8584.
  25. Crainic. Marius. Fernandes. Rui. 2003-03-01. Integrability of Lie brackets. Annals of Mathematics. 157. 2. 575–620. 10.4007/annals.2003.157.575. 0003-486X. free. math/0105033.
  26. Crainic. Marius. Fernandes. Rui Loja. 2011-03-01. A geometric approach to Conn's linearization theorem. Annals of Mathematics. 173. 2. 1121–1139. 10.4007/annals.2011.173.2.14. 0003-486X. free. 0812.3060.
  27. Crainic. Marius. Abad. Camilo Arias. 2011-06-17. Representations up to homotopy of Lie algebroids. Journal für die reine und angewandte Mathematik. 2012. 663. 91–126. 10.1515/CRELLE.2011.095. 18662057. 0075-4102.
  28. Crainic. Marius. Abad. Camilo Arias. The Weil algebra and the Van Est isomorphism. Annales de l'Institut Fourier. 61 (2011). 3. 927–970. 10.5802/aif.2633. 2011. free. 0901.0322.
  29. Web site: Marius Crainic - Google Scholar Citations. scholar.google.nl. 2020-02-01.

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