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]

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]