Curriculum Vitae for Marius Crainic
Curriculum Vitae for Marius Crainic
Curriculum Vitae for Marius Crainic
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
<strong>Curriculum</strong> <strong>Vitae</strong> <strong>for</strong> <strong>Marius</strong> <strong>Crainic</strong><br />
Personal<br />
Name:<br />
<strong>Marius</strong> Nicolae <strong>Crainic</strong><br />
Date of Birth: February 3, 1973<br />
Place of Birth:<br />
Aiud (Romania)<br />
Nationality:<br />
Romanian<br />
Marital Status:<br />
Married (2 children).<br />
Home address:<br />
Dennenhorst 30, 3972 GM, Driebergen-Rijsenburg<br />
Work address:<br />
Wiskunde Gebouw, Budapestlaan 6, 3584 CD, Utrecht, Holland<br />
Web-page:<br />
http://www.math.uu.nl/people/crainic/<br />
Email:<br />
m.crainic@uu.nl<br />
Tel.: +31 30 2531429<br />
Fax: +31 30 2518394<br />
Education<br />
1996- 2000 Ph.D., Utrecht University<br />
Thesis: “Cyclic cohomology and characteristic classes <strong>for</strong> foliations”.<br />
Adviser: Ieke Moerdijk.<br />
1995-1996 M.Sc. in Mathematics, MRI Master-Class Programme, Katholieke Univ. Nijmegen.<br />
Thesis: “Algebraic K-theory of quadratic number rings”.<br />
Mark of the final dissertation: 9.50.<br />
1991-1995 B.S. in Mathematics, “Babes-Bolyai” University, Cluj-Napoca, Romania.<br />
Diploma thesis:“The Atiyah-Singer index theorem and the Atiyah-Bott<br />
Average mark: 10 (maximum).<br />
1987-1991 High School, “H.C.C.” High School, Alba Iulia, Romania.<br />
The rest of this <strong>Curriculum</strong> <strong>Vitae</strong> is made out of three parts:<br />
• Research Component (containing Experience; Grants and Awards; International Activities;<br />
Organizational Activities).<br />
• Teaching Component (containing Teaching Degrees; Mini-courses abroad; Teaching<br />
Experience; Supervising Experience).<br />
• Publications Component.
<strong>Curriculum</strong> <strong>Vitae</strong> <strong>for</strong> <strong>Marius</strong> <strong>Crainic</strong><br />
I. Research Component:<br />
Summary:<br />
• Experience<br />
• Grants and Awards<br />
• Talks in (international) conferences<br />
• Organizational activities<br />
• The broad research interests of <strong>Marius</strong> <strong>Crainic</strong>: Geometry and Topology<br />
3
Experience<br />
2007- UHD , Utrecht University, The Netherlands.<br />
2002-2007 UD , Utrecht University, The Netherlands.<br />
2002- 2007 Research Fellow of the Dutch Royal Academy of Sciences.<br />
Febr 2007<br />
May 2003<br />
Invited Professor, Institute Henri Poincare, Paris, France.<br />
Invited Professor, University of Clairmont-Ferrant, France.<br />
2001- 2002 Miller Research Fellow, University of Cali<strong>for</strong>nia at Berkeley, USA.<br />
2000- 2001 Post Doc position, Utrecht University, The Netherlands.<br />
1999 6 months visiting position, Universite Paris 6, France.<br />
1996- 2000 Ph.D. Research, Utrecht University.<br />
5
Grants and Awards 1<br />
2011-2016 ERC Starting Grant “New Advances through the boundaries of Poisson Geometry”.<br />
This project funds several PhD and PostDoc positions and is carried out at UU.<br />
The support <strong>for</strong> the project is 1.1 mil. euro.<br />
2011-2016 NWO Vrije Competitie project “Flexibility and Rigidity of Geometric Structures”.<br />
This project funds a PostDoc position (3 years) and is carried out at UU.<br />
The support <strong>for</strong> the project is 200 k euro.<br />
2009-2013 NWO Vrije Competitie project “Geometry of PDE’s and Poisson structures”.<br />
This project funds a PostDoc position (3 years) and is carried out at UU.<br />
The support <strong>for</strong> the project is 200 k euro.<br />
2009 The SKOz degree (Senior Research Qualification), Utrecht University.<br />
2008 Andre Lichnerowicz Prize in Poisson Geometry<br />
Lausanne, July 2008.<br />
2007-2012 NWO Vidi project “Poisson Topology”.<br />
This project funds a PhD position (4 years), a PostDoc position (3 years),<br />
and part of my salary (about 2/3) and is carried out at Utrecht University.<br />
The support <strong>for</strong> the project is 600 k euro.<br />
2004-2008 NWO Open Competitie project “Symmetries and De<strong>for</strong>mations in Geometry”.<br />
This project funded a PhD position (4 years) + a PostDoc position (3 years) at UU.<br />
The support <strong>for</strong> the project is 352 k euro.<br />
2002- 2007 KNAW Research Fellowship.<br />
The grant was awarded <strong>for</strong> 3 years, and then prolonged <strong>for</strong> another 2.<br />
The grant supported my research and was carried out at Utrecht University.<br />
The support <strong>for</strong> the project is around 350 k euro.<br />
2001-2004 Miller Research Fellowship (interrupted half way to start the KNAW position).<br />
The grant supported my research position at UC Berkeley. Applications <strong>for</strong> the grant<br />
are only by invitation and the selection is from all fields in science.<br />
1996-2000 NWO PhD Fellowship, Utrecht University.<br />
1995-1996 Master Class Fellowship, Mathematical Research Institute, The Netherlands.<br />
1998-1991 Olympiads: various awards at national and international“Olympiads” such as:<br />
- International Mathematics Olympiad, Beijing, 1990: 3 rd prize.<br />
- Balkan Mathematics Olympiad: 1 st prize in 1990 and 1991.<br />
- National Mathematics Olympiad (Romania): 1 st prize in 1991; 2 nd prize in 1990.<br />
1 NWO= The Dutch National Science Foundation; KNAW= The Dutch Royal Academy of Arts and Sciences;<br />
MRI= The Dutch Mathematical Research Institute; Miller: refers to the Miller Foundation <strong>for</strong> Fundamental<br />
Research in Sciences, at UC Berkeley<br />
7
Talks in (international) conferences<br />
• Oberwolfach meetings (Germany): several participations/talks given at the workshops<br />
organized at Mathematisches Forschungsinstitut Oberwolfach where the participation was<br />
by invitation only:<br />
- “Noncommutative Geometry”, September 2011.<br />
- “Poisson Geometry and Applications”, April-May 2007.<br />
- “Quantization of Poisson spaces with singularities”, January 2003.<br />
- “Nichtkommutative Geometrie”, March 2002.<br />
- “Noncommutative Geometry”, October 2001.<br />
- “Nichtkommutative Geometrie”, March 2000.<br />
- “Nichtkommutative Geometrie”, August 1998.<br />
• Erwin Schrodinger Institute <strong>for</strong> Mathematical Physics (Viena): invited to participate<br />
to various programs held at ESI and give talks in the related conferences, such<br />
as:<br />
- invited to the program “Higher structures in Mathematics and Physics”, October<br />
2010.<br />
- invited to the workshop “Poisson Geometry and Sigma-models”, August 2007.<br />
- invited to the program “Poisson sigma-models, Lie algebroids, de<strong>for</strong>mations and<br />
higher analogues”, 2007.<br />
- invited <strong>for</strong> the program “Gerbes, Groupoids, and Quantum Field Theory”, May 2006.<br />
- invited <strong>for</strong> the program “Moment maps and Poisson geometry”, August-November<br />
2003.<br />
- invited to the program “Aspects of Foliation Theory in Geometry, Topology and<br />
Physics”, September 2002.<br />
• Poisson conferences: invited to speak in the regular biennial conference in Poisson<br />
geometry:<br />
- “Poisson Geometry in Mathematics and Physics”, IMPA, Rio de Janeiro, July 2010.<br />
- “Poisson Geometry in Mathematics and Physics”, Bernoulli Center, Lausanne, Switzerland,<br />
July 7-11, 2008.<br />
- “Poisson geometry in mathematics and physics”, Tokyo, June 2006.<br />
- “Poisson 2004”, Luxembourg, June 2004,<br />
- “Poisson 2002”, Lisbon, September 2002.<br />
• Higher Structures conferences: invited to speak in the regular conferences ion ”higher<br />
structures”:<br />
- “Higher structures”, Gottingen, November, 2011.<br />
- “Higher structures in Mathematics and Physics”, Viena, October 2010.<br />
- “Higher Structures in Mathematics and Physics”, Zurich, November 2009.<br />
• MSRI (Berkeley):<br />
Berkeley:<br />
invited to speak in various conferences organized at the MSRI at<br />
9
- “Symplectic geometry, noncommutative geometry and physics”, 2010.<br />
- “Noncommutative Geometry and quantization”, 2001.<br />
• Other conferences: invited to speak in various other conferences such as:<br />
- “Poisson Geometry and Applications”, Figueira da Foz, June 2011.<br />
- “Quantization of Singular Spaces”, Aarhus, December 2010.<br />
- “XVIII International Fall Workshop on Geometry and Physics”, Centro de Ciencias<br />
de Benasque Pedro Pascual, September 2009.<br />
- “FNRS contact group in Differential Geometry”, Han-sur-Lesse, Belgium, November<br />
2008.<br />
- “Symplectic Geometry with Algebraic Techniques” (GESTA 2008), CRM Barcelona,<br />
May 2008.<br />
- “Lie Algebroids and Lie Groupoids in Differential Geometry”, Sheffield, 2007.<br />
- “Conference on Poisson Geometry”, the the Abdus Salam International Centre <strong>for</strong><br />
Theoretical Physics, Trieste, July 2005.<br />
- “Au-dela des algebroides de Lie”, École Polytechnique, 2004.<br />
- “Poisson Geometry, De<strong>for</strong>mation Quantisation and Group Representations”, Brussels,<br />
June 2003.<br />
- “Groupoid-fest 2002”, Reno, Nevada, November 2002.<br />
- “Quantization, de<strong>for</strong>mations, and new homological and categorical methods in mathematical<br />
physics”, LMS meeting, Manchester, 2001.<br />
- “Symplectic Geometry and Microlocal Analysis”, Penn State University, 1999.<br />
• Other visits, talks and minicourses: several other visits abroad, such as: University<br />
of Geneva (October 2007, invited by A. Alekseev and A. Heafliger), IHP Paris (January<br />
2007), CIRM Luminy (September 2007), Instituto Superior Tecnico, Lisbon, Portugal<br />
(several visits in 2001, 2005, 2006, 2007, invited by R.L. Fernandes), Universite Paul<br />
Sabatier (Toulouse, 2002), University of Muenster (2002), University of Cali<strong>for</strong>nia at Los<br />
Angeles (UCLA, 2001), etc. In all cases, I was invited to give talks or mini-courses (<strong>for</strong><br />
the detailed list of mini-courses, see the ”teaching component” of the CV).<br />
• Journals: editor <strong>for</strong> the journals Indagationes and Mathematica; also a referee <strong>for</strong> various<br />
journals such as Journal of Differential Geometry, Inventiones, Advances in Mathematics,<br />
Duke Mathematical Journal, J. Reine Angew. Math., American Journal of Mathematics,<br />
Journal of Symplectic Geometry, Pacific Journal of Mathematics, Annales de l’institut<br />
Fourier, K-Theory etc.<br />
• Berkeley activities: During my stay at UC Berkeley as a Miller Research Fellow, I<br />
participated in various activities in the region (MSRI, Stand<strong>for</strong>d, UCLA) andas well as<br />
in the weekly interdisciplinary colloquium organized by the Miller Foundation <strong>for</strong> Basic<br />
Research in Science, which brings together scientists from the exact sciences.<br />
10
Organizational activities<br />
• Poisson 2012: I am the chair of the organizing committee <strong>for</strong> the conference and summer<br />
school “Poisson 2012”, where we expect over 200 participants. Please see<br />
www.math.uu.nl/poisson2012<br />
• Scientific organizer: organized various national or international activities such as:<br />
- The GQT conference “Conference Geometry and Quantum Theory” (together with G.<br />
Heckman and J. Heinlot), marking the end of the GQT cluster (June 2008, Nijmegen).<br />
- The meeting “TopoLogical Workshop”, obtaining the financial support from the MRI<br />
and NWO (April 2008, at the conference center Bergse Bos in Driebergen).<br />
- The workshop “Alan’s day” , in relation with the honorary doctorate awarded by the<br />
University of Utrecht to Alan Weinstein (March 2003, Utrecht).<br />
- Co-organizer of the Oberwolfach meeting “Poisson Geometry and applications” (May<br />
2007) .<br />
- Member of the Scientific Committee <strong>for</strong> the conference “Poisson 2010”.<br />
- The scientific organizer of the 2006/2007 Master Class entitled “Symplectic geometry<br />
and Beyond”.<br />
- Involved in the scientific organization of the 2003/2004 Master Class entitled “Noncommutative<br />
geometry”.<br />
- Organized/co-organized various local and national seminars on Topology, Poisson Geometry,<br />
Noncommutative Geometry, Mathematical Physics. E.g., in 2007: Floer Homology<br />
Seminar (together with D. Martinez Torres), in September 2008 I started the<br />
“Friday Fish Seminar” (see http://www.math.uu.nl/people/crainic/Poisson/index.html),<br />
etc etc (2000- present).<br />
• Olympiad (2009- ) Various tasks related to the Dutch Mathematical Olympiads <strong>for</strong> highschool<br />
students. I became more and more interested and involved in such activities. I<br />
have several ideas and plans in this direction, such as establishing long-term connections<br />
between universities and high-schools, creating new opportunities <strong>for</strong> interactions between<br />
the best high-school teachers, at the national level, etc etc. In particular, we have introduced<br />
the ”Tweede Ronde”, which is a regional round be<strong>for</strong>e the ”final”, together with<br />
“training sessions” that are organized by various universities throughout the country. In<br />
this direction, I am in coordinating all the activities <strong>for</strong> the Utrecht region, such as the<br />
organization each year of the regional round <strong>for</strong> Utrecht. In July 2011, I was one of the<br />
coordinators at the IMO (international Mathematics Olympiad) that took place in The<br />
Netherlands.<br />
• Master Class (2004- 2009): Coordinator of the “Master Class” programme of the Dutch<br />
Mathematical Research Institute.<br />
The MRI is founded by the universities of Groningen, Nijmegen, Twente and Utrecht. The<br />
Master Class programme aimed at attracting bright students from abroad to come and<br />
study in the Netherlands, to stimulate the interaction between the students (<strong>for</strong>eign as<br />
well as Dutch), and to offer each year a package of courses that cover an important field<br />
of Mathematics and Mathematical Physics and brings the students to the level of starting<br />
with PhD research.<br />
The role of the coordinator is to supervise the ongoing master classes (schedule, various<br />
11
activities, final ceremony, etc), to attract new MC proposals, to advertise the program, to<br />
select the students etc. Master Classes coordinated:<br />
– Arithmetic Geometry and Noncommutative Geometry (2009-2010)<br />
– Numerical Bifurcation Analysis of Dynamical Systems (2009-2010)<br />
– Calabi-Yau geometry (2008-2009)<br />
– Quantum groups, affine Lie algebras and applications (2007-2008)<br />
– Symplectic geometry and Beyond (2006-2007) (Also Scientific organizer).<br />
– Logic (2006-2007).<br />
– Finite and infinite dimensional dynamical systems (2005-2006).<br />
– Stochastics in Molecular Biology and Genetics (2004-2005).<br />
There are several main achievements in this direction:<br />
– During this period, the Master Class obtained the financial support of the various<br />
dutch clusters (most notably, the GQT cluster supports each year about 8 students,<br />
<strong>for</strong> a period of 6 years). The survival of the Master Class depends on finding such<br />
financial support.<br />
– The Master Class program made it into the academic news (when, at the opening of<br />
the GQT cluster, the Ministry of Education spoke about the importance of the MC<br />
and handed out to the students their diplomas).<br />
– As a step in advertising the programme, I made a new data-base (up-to-date and<br />
complete) containing the main Mathematics Departments around the world and their<br />
addresses. This data base is nowadays used by the entire department <strong>for</strong> advertising<br />
various other programs.<br />
– I started another data-base, containing the names and the whereabouts of the <strong>for</strong>mer<br />
Master Class students. This in<strong>for</strong>mation was already used by NWO in some of their<br />
public presentations (serving as an interesting analysis from various points of view:<br />
the role of <strong>for</strong>eign students coming and studying in Holland, the extremely varied<br />
career paths taken by them).<br />
• Stafcolloquium (UU) (2004-2008): Organizer of the general (weekly) Stafcolloquium<br />
of the Mathematics Department, Utrecht University, together with G. Cornelissen (until<br />
2006/2007) and with R. Bisseling (remaining period). The duties include the process of<br />
finding and inviting speakers, managing the Stafcolloquium funds, etc.<br />
• Memberships, committees:<br />
- Member of the national research commission (“Commissie Onderzoek”) of the PWN<br />
(since 2010).<br />
- Editor <strong>for</strong> the journal Indagationes (since 2010).<br />
- Editor <strong>for</strong> the journal Mathematica (since 2009)<br />
- Part of various selection committees, such as the one <strong>for</strong> the UD position at UU<br />
associated to the GQT cluster (2008), or the Vrije Competitie selection committees<br />
<strong>for</strong> 2010 and 2012.<br />
12
The broad research interests of <strong>Marius</strong> <strong>Crainic</strong>: Geometry and Topology<br />
Geometry is the oldest branch of mathematics. It is concerned with questions of shape, size,<br />
relative position of figures, and the properties of space. Its empirical origins were put into an<br />
axiomatic <strong>for</strong>m by Euclid (3rd century BC ), and the resulting Euclidean geometry has been<br />
standard <strong>for</strong> many centuries. Questions from astronomy, on the position and the movement<br />
of stars and planets, served as an important source of geometric problems during one and a<br />
half millennia. The discovery of coordinates by Ren Descartes played an essential role in the<br />
development of algebra (geometric figures, such as plane curves, could now be represented by<br />
equations) and, later on, in the emergence of infinitesimal calculus in (17th century). For a<br />
long time, there was no clear distinction between physical space and geometrical space; starting<br />
with the discovery of non-Euclidean geometry (19th century) the notion of “geometric space”<br />
has undergone a radical trans<strong>for</strong>mation (up to the point that even notions like “space”, “point”,<br />
“line” etc lost their original intuitive content). The central question became: which “abstract”<br />
geometrical space best fits (models) the physical space.<br />
Differential Geometry: Contemporary geometry considers manifolds- which are spaces that<br />
approximately resemble the familiar Euclidean space only at small scales (e.g. spheres). On<br />
these, one considers various “geometric structures”, depending on the aspects one is interested<br />
in. Differential Geometry is the resulting study of manifolds endowed with such geometric<br />
structures. For instance, to talk about “lengths”, the geometric structure that one has to<br />
consider is known under the name of “Riemannian metric” and the resulting field is known as<br />
“Riemannian Geometry” (a subfield of Differential Geometry). Differential geometry is also the<br />
language in which Einstein’s general theory of relativity is expressed: the universe appears as a<br />
smooth manifold equipped with a pseudo-Riemannian metric, which describes the curvature of<br />
space-time; understanding this curvature is essential <strong>for</strong> the positioning of satellites into orbit<br />
around the earth. One may even say that each physical theory comes with its own (subfield<br />
of) geometry. Another example comes from the Hamiltonian <strong>for</strong>mulation of classical mechanics,<br />
which gives rise to Poisson Geometry. In this theory, the objects that are studied are manifolds<br />
endowed with the geometric structures that allows one to write down Hamilton’s equations<br />
(“Poisson structures”).<br />
We also have to mention here that role played by symmetries in geometry. When looking at most<br />
of Eschers drawings, one realizes the presence of symmetry, which allows one to reconstruct the<br />
complete drawing from a smaller part of it. More generally, one of the central ideas in geometry<br />
is to understand (and even classify) the geometric objects via their ”symmetries”; this originates<br />
in Klein’s Erlanger Programm (1872). The precise mathematical notion that allows us to talk<br />
about symmetries in Differential Geometry is that of “Lie group”. Its birth goes back to the<br />
work of Sophus Lie on symmetries of differential equations (at the end of the nineteenth century)<br />
and that of Elie Cartan on symmetries of geometric structures (at the beginning of the twentieth<br />
century). Nowadays one talks about “Lie Theory”, which pervades modern mathematics and<br />
theoretical physics.<br />
Topology: A close relative of Geometry is the field of “Topology”, which is concerned with<br />
properties that are preserved under continuous de<strong>for</strong>mations of objects, such as de<strong>for</strong>mations<br />
that involve stretching, but no tearing or gluing. For instance, a circle and an ellipsis, although<br />
geometrically distinct, have the same topology: one can be obtained from the other by a continuous<br />
trans<strong>for</strong>mation- realise the ellipsis as the shadow of a non-horizontal circle and consider the<br />
trans<strong>for</strong>mation along the rays of light. Similarly, spheres and convex polyhedra are topologically<br />
similar; as a consequnce, one arrises at the famous theorem of Euler which says that, <strong>for</strong> any<br />
13
convex polyhedra, the Euler characteristic (i.e. the number of faces minus the number of edges<br />
plus the number of vertices) is allways 2. In relation with geometry, one should keep in mind<br />
that every field in geometry comes with its underlying topological aspects, and one of the most<br />
fundamental mathematical question is to understand the effect that the topology has on the<br />
geometry. Probably one of the best known examples of this interaction is the Gauss-Bonnet<br />
theorem which relates the curvature of a surfaces (defined using Riemannian metrics, hence Differential<br />
Geometry) in terms of the Euler characteristic (defined using Topology). The modern<br />
generalization of the Gauss-Bonnet theorem, known as the Atiyah-Singer index theorem, brings<br />
together in an exciting way Topology, Geometry as well as Analysis, with striking applications<br />
to Mathematical Physics.<br />
In a broad sense, the research interests of <strong>Marius</strong> <strong>Crainic</strong> are in the field of Differential Geometry<br />
and its interactions with Topology. More specific current interests are in the field of Poisson<br />
Geometry and in the modern aspects of Lie theory (see above). In fact, MC is best known<br />
<strong>for</strong> his results on integrability (solving a long-standing open problem in Lie theory), and his<br />
contributions to Poisson Geometry (including the solution to some other problems that were<br />
open <strong>for</strong> a long time, <strong>for</strong> which he was awarded the ”Lichnerowicz prise” in 2008). Currently he<br />
is working on developping the new field of “Poisson Topology” and on the study of geometric<br />
structures (such as Poisson structures, but not only) as well as of partial differential equations<br />
using his own insight in Lie Theory (via Lie pseudogroups and Lie groupoids).<br />
14
<strong>Curriculum</strong> <strong>Vitae</strong> <strong>for</strong> <strong>Marius</strong> <strong>Crainic</strong><br />
II. Teaching and Supervising Component<br />
Summary:<br />
• Teaching education/degrees<br />
• At the border of research/teaching: mini-courses abroad<br />
• Teaching experience (at UU)<br />
• PhD supervision<br />
• Other supervising experience<br />
15
Teaching education/degrees<br />
1995: The degree of “Mathematics Teacher”, Babes-Bolyai University, Romania.<br />
The degree was awarded at the end of the B.S. studies, and the education included<br />
standard courses such as Pedagogy, Psychology, Methodology, etc,<br />
as well as practical training in high schools and Olympiad camps.<br />
2008: The BKO degree (Basic Teaching Qualification), Utrecht University.<br />
2008: The SKO degree (Senior Teaching Qualification), Utrecht University.<br />
17
At the border of research/teaching: mini-courses abroad<br />
Here are some mini-courses that I was invited to give:<br />
February 2010 Les Diablerets, Switzerland: invited to give a<br />
minicourse in the “Winter School on Mathematical Physics”<br />
July 2008<br />
May 2008<br />
Bernoulli Center, Lausanne, Switzerland: invited to give a<br />
minicourse in the Poisson 2008 Summer School (July 1-7) in the<br />
“Poisson Geometry in Mathematics and Physics” program.<br />
Centre de Recerca Matematica, Barcelona: invited to give a<br />
minicourse (21- 24 May) in the “Geometric Flows. Equivariant Problems in<br />
Symplectic Geometry” program .<br />
Jan-Apr 2007 IHP, Paris: introductory minicourse on symmetries of<br />
differential equations, Lie pseudogroups and groupoids, in the<br />
“Groupoids and Stacks in Physics and Geometry” program.<br />
Sept 2007<br />
July 2005<br />
CIRM, Luminy: introductory minicourse on cohomology of groupoids,<br />
non-commutative geometry and cyclic cohomology,<br />
in the “Aperiodic orders” program.<br />
Abdus Salam International Centre <strong>for</strong> Theoretical Physics (ICTP),<br />
Trieste, Italy: course on “Lie algebroids and groupoids, and<br />
applications”, and preparing lecture notes (together with RL Fernandes).<br />
2004 Ecole Polytechnique, Paris: minicourse on “Momentum maps”.<br />
June 2003<br />
March 2002<br />
Clairmont-Ferrant, France: minicourse on “The integrability problem and<br />
applications”, in the “Journees Mathematique Et Physique Clermont/Lyon” .<br />
Universite Paul Sabatier, Toulouse, France: minicourse on “Integrability<br />
of Lie algebroids”.<br />
19
Teaching experience (at UU)<br />
2012- 2013 (scheduled) Teaching the course “Analysis on manifolds” (with E.v.d. Ban).<br />
This is a master level course <strong>for</strong> the Mathematics students.<br />
2011- 2012 Teaching the course “Differential Geometry”.<br />
This is a course in the National Master program.<br />
2011- 2012 Teaching the course “Inleiding Topologie”.<br />
This is a bachelor course <strong>for</strong> our 2nd year students.<br />
Please see the web-page: http://www.staff.science.uu.nl/ crain101/topologie12/.<br />
2010- 2011 Developing and teaching the new course “Inleiding Topologie”.<br />
This is a new bachelor course <strong>for</strong> our 2nd year students.<br />
Please see the web-page: http://www.staff.science.uu.nl/ crain101/topologie11/.<br />
2010- 2011 Teaching and revising the standard course “Geometry and Topology”.<br />
This is a third level course <strong>for</strong> the Mathematics students.<br />
Please see the web-page: http://www.staff.science.uu.nl/ crain101/meetkunde11/.<br />
2009- 2010 Teaching the course “Analysis on manifolds” (with E.v.d. Ban).<br />
This is a master level course <strong>for</strong> the Mathematics students.<br />
2008- 2009 Teaching the course “Geometry and Topology” following my own lecture notes.<br />
This is a third level course <strong>for</strong> the Mathematics students.<br />
Please see the web-page: http://www.math.uu.nl/people/crainic/topologie09/ .<br />
2007- 2008 Teaching the course “Geometry and Topology”, and revising my own lecture notes.<br />
This is a third level course <strong>for</strong> the Mathematics students.<br />
Please see the web-page: http://www.math.uu.nl/people/crainic/topologie08/ .<br />
2007-2008 Teaching the course “Group theory”.<br />
This is a second level course <strong>for</strong> the Mathematics students.<br />
Please see the web-page: http://www.math.uu.nl/people/crainic/groups2007/.<br />
2006- 2007 Supervising the Master Class seminar, together with D.M.Torres,<br />
on Lie groupoids and Lie algebroids, using<br />
my own lectures notes written together with R.L. Fernandes.<br />
2006- 2007 Teaching the course “Geometry and Topology”, and revising my own lecture notes.<br />
This is a third level course <strong>for</strong> the Mathematics students.<br />
Please see the web-page: http://www.math.uu.nl/people/crainic/topologie07/ .<br />
2006- 2007 Developing and teaching the course “Poisson geometry”, first taught in the<br />
2006- 2007 Master Class programme, and writing lecture notes.<br />
(together with H. Bursztyn).<br />
2005- 2006 Teaching and revising the standard course “Geometry and Topology”,<br />
and preparing lecture notes (which were improved in the last several years).<br />
This is a third level course <strong>for</strong> the Mathematics students.<br />
21
Please see the web-page: http://www.math.uu.nl/people/crainic/topologie/.<br />
2003- 2004 Developing and teaching the course “Cyclic cohomology”, first taught in the<br />
2003- 2004 Master Class programme, and writing lecture notes.<br />
Please see http://www.math.uu.nl/people/crainic/curs.ps.<br />
2003- 2004 Supervising the (undergraduate) student seminar on Frobenius<br />
algebras (together with I. Moerdijk),<br />
2003- 2004 Supervising the Master Class seminar, together with I. Moerdijk,<br />
on Algebraic Topology.<br />
1999- 2000 Exercise classes ”Differential Geometry” taught by E. Looijenga.<br />
1996-present<br />
Occasional replacements in teaching.<br />
22
PhD supervision<br />
2012-2017 Supervising Roy Wang (PhD student at UU)<br />
supported by by my ERC grant.<br />
Subject: to be determined.<br />
Starting date: January 1st, 2012.<br />
2011-2015 Supervising Ori Yudilevich (PhD student at UU)<br />
supported by by my ERC grant.<br />
Subject: to be determined.<br />
Starting date: October 1, 2011.<br />
2010-2014 Supervising Boris Osorno Torres (PhD student at UU)<br />
supported by by my Vidi project (Poisson Topology) and my ERC grant.<br />
Subject: proper actions, singular spaces.<br />
Starting date: September 1, 2010.<br />
2010-2014 Supervising Joao Nuno (PhD student at UU)<br />
supported by a grant from the Portuguese Science Foundation.<br />
Subject: proper actions, singular spaces.<br />
Starting date: September 1, 2010.<br />
2009-2013 Supervising Maria A. Salazar (PhD student at UU) ,<br />
supported by the NWO GQT cluster (3/4) and UU department (1/4).<br />
Subject: The geometry of partial differential equations.<br />
Starting date: January 1, 2009.<br />
2008-2012 Supervising Ionut Marcut (PhD student at UU)<br />
supported by my Vidi project (Poisson Topology).<br />
Subject: Poisson Geometry and Topology.<br />
Starting date: September 1, 2008.<br />
2006-2009 Supervised Niels Kowalzig (PhD student at UU),<br />
supported by the GQT cluster (national ressearch cluster).<br />
Subject: noncommutative geometry (cyclic cohmology, Hopf algebras).<br />
Thesis defense: June 30, 2009.<br />
2004-2008 Supervised C. Arias Abad (PhD student at UU) ,<br />
supported by my Open Competitie project “Symmetries<br />
and De<strong>for</strong>mations in Geometry”.<br />
Subject: topology, differential geometry (equivariant cohomology,<br />
Cartan models, classyfying spaces).<br />
Thesis defense: December 8, 2008.<br />
2000- 2002 Involved in the supervision of a PhD student of A. Weinstein (C. Zhu)<br />
at UC Berkeley.<br />
23
Other supervising experience<br />
2011-2013 Hosting/supervising Florian Schaetz (PostDoc at UU)<br />
supported by my ERC project .<br />
2011-2014 Hosting/supervising Pedro Frejlich (PostDoc at UU)<br />
supported by my Vrije Competitie project<br />
“Flexibility and Rigidity of Geometric Structures” .<br />
2010-2013 Hosting/supervising Sergey Igonin (PostDoc at UU)<br />
supported by my Vrije Competitie project<br />
“Geometry of PDEs and Poisson structures” .<br />
2009-2012 Hosting/supervising Ivan Struchiner (PostDoc at UU)<br />
supported by my Vidi project “Poisson Topology”.<br />
2005-2008 Hosting/supervising David Martinez Torres (PostDoc at UU)<br />
and Henrique Bursztyn (one year visitor), supported by my Open Competitie<br />
project “Symmetries and De<strong>for</strong>mations in Geometry”.<br />
2010-2011 Supervising the Master Thesis of Roy Wang<br />
(The Nash-Moser implicit function theorem and applications).<br />
2010-2011 Supervising the Master Thesis of Marcel de Reus<br />
(Introduction to Functional Spaces).<br />
2007-2008 Supervising the Master Thesis of Janne Kool<br />
(Fibrations in symplectic and Poisson geometry).<br />
2009- 2010 Supervising the Master Thesis of Roy Wang.<br />
2009- 2010 Supervising the ”kleine scriptie” of Tim Zwart.<br />
2008- 2009 Supervising the ”kleine scriptie” of Roy Wang.<br />
2008- 2009 Supervising the ”kleine scriptie” of Jori Matthijssen.<br />
2006- 2008 Supervising several groups of undergarduate students <strong>for</strong><br />
their “Werkstuk” (in the “Kaleidoscoop”).<br />
2006- 2007 Supervising the final Master Class thesis of Yunjiang Jiang<br />
(“Action-angle coordinates and generalizations”).<br />
2006- 2007 Supervising the final Master Class thesis of Josef Pozny<br />
(“Singular foliations”).<br />
2003- 2004 Supervising the final Master Class thesis of Camilo Arias Abad<br />
(“Serre spectral sequences <strong>for</strong> Lie algebroids”).<br />
2003- 2004 Supervising the final Master Class thesis of A. Quintero Velez<br />
24
<strong>Curriculum</strong> <strong>Vitae</strong> <strong>for</strong> <strong>Marius</strong> <strong>Crainic</strong><br />
III. Publications Component<br />
26
Publications<br />
1. Main published papers (geometry)<br />
[1] Representations up to homotopy of Lie algebroids, joint work with C. Arias Abad,<br />
Journal fur die reine und angewandte Mathematik 663 (2012), 91–126<br />
[2] A geometric approach to Conn’s linearization theorem, joint work with R.L. Fernandes,<br />
Annals of Mathematics 173 (2011), 1121-1139.<br />
[3] The Weil algebra and van Est isomorphisms, joint work with C. Arias Abad,<br />
Annales de L’Institut Fourier 61 (2011), 927-970<br />
[4] On the existence of symplectic realizations, joint work with I. Marcut,<br />
Journal of Symplectic Geometry 9 (2011), 435-444<br />
[5] Tensor products of representations up to homotopy, joint work with C. Abad and B. Dherin.<br />
J. Homotopy Relat. Struct. 6 (2011), 239-288<br />
[6] Stability of symplectic leaves, joint work with R.L. Fernandes,<br />
Inventiones Math. 180, no. 3, (2010), 481-533.<br />
[7] Dirac geometry and quasi-Poisson actions, joint work with H. Bursztyn,<br />
Journal of of Differential Geometry 82 (2009), 501-566.<br />
[8] De<strong>for</strong>mations of Lie brackets: cohomological aspects, joint work with Ieke Moerdijk,<br />
Journal of European Mathematical Society, 10 no. 4 (2008), pp. 1037-1059.<br />
[9] Integrability of Jacobi and Poisson structures, joint work with Chenchang Zhu,<br />
Annales de l’institut Fourier, 57 no. 4 (2007), pp. 1181-1216.<br />
[10] Integration of twisted Dirac brackets, joint work with H. Bursztyn, A. Weinstein, C. Zhu ,<br />
Duke Math. J. 123 (2004), pp. 549–607<br />
[11] Prequantization and Lie brackets,<br />
J. Symplectic Geom. 2 (2004), pp. 579–602<br />
[12] Integrability of Poisson brackets, joint work with R.L. Fernandes,<br />
J. Differential Geom. 66 (2004), pp. 71–137<br />
[13] Cech-De Rham theory <strong>for</strong> leaf spaces of foliations, joint work with I. Moerdijk,<br />
Math. Ann. 328 (2004), pp. 59–85<br />
[14] Integrability of Lie brackets, joint work with R.L. Fernandes,<br />
Annals of Mathematics 157 (2003), pp. 575–620<br />
[15] Differentiable and algebroid cohomology, van Est isomorphisms, and characteristic classes,<br />
Comment. Math. Helv. 78 (2003), pp. 681–721<br />
[16] Cyclic cohomology of Hopf algebras,<br />
J. Pure Appl. Algebra 166 (2002), pp. 29–66<br />
[17] Foliation groupoids and their cyclic homology, joint work with I. Moerdijk,<br />
Advances in Mathematics 157 (2001), pp. 177–197<br />
[18] A homology theory <strong>for</strong> etale groupoids, joint work with I. Moerdijk,<br />
J. Reine Angew. Math. 521 (2000), pp. 25–46<br />
28
[19] Cyclic cohomology of etale groupoids: the general case,<br />
K-Theory 17 (1999), pp. 319–362<br />
2.To appear (refereed)<br />
[20] The Bott spectral sequence <strong>for</strong> classifying spaces, joint work with C. Arias Abad,<br />
Advances in Mathematics, to appear.<br />
[21] A Normal Form Theorem around Symplectic Leaves, joint work with I. Marcut,<br />
Journal of Differential Geometry, to appear.<br />
[22] On the linearization theorem <strong>for</strong> proper Lie groupoids, joint work with I. Struchiner,<br />
Annales scientifiques de l’Ecole normale superieure , to appear.<br />
3.Proceedings (refereed)<br />
[23] Lectures on integrability of Lie brackets, joint work with R.L. Fernandes,<br />
Geom. Topol. Monogr., 17 (2011), 1–107<br />
[24] Generalized complex structures and Lie brackets,<br />
Bulletin of the Brazilian Mathematical Society 42 (2011), 559-578.<br />
[25] Secondary characteristic classes of Lie algebroids, joint work with R.L. Fernandes,<br />
Quantum field theory and noncom. geom., Lecture Notes in Phys. 232 (2005), pp. 157–176<br />
[26] Rigidity and flexibility in Poisson geometry,joint work with R.L. Fernandes,<br />
Travaux mathematiques. Fasc. XVI, 53–68, Trav. Math., XVI, Univ. Luxemb. (2005).<br />
[27] Quasi-Poisson structures as Dirac structures, joint work with H. Bursztyn and P. Severa,<br />
Travaux matheatiques. Fasc. XVI, 41–52, Trav. Math., XVI, Univ. Luxemb. (2005)<br />
[28] Dirac structures, momentum maps, and quasi-Poisson manifolds, joint with H. Bursztyn,<br />
The breadth of symplectic and Poisson geometry, Progr. Math. 157 (2005), pp. 1–40<br />
4.Other papers (refereed)<br />
[29] Birkhoff Interpolation with Rectangular Sets of Nodes, joint with N. <strong>Crainic</strong>,<br />
Journal of Numerical Mathematics, 2010.<br />
[30] Polya conditions <strong>for</strong> multivariate Birkhoff interpolation: from general to rectangular sets<br />
of nodes, joint with N. <strong>Crainic</strong>,<br />
Acta Mathematica Universitatis Comenianae, 2010.<br />
[31] Normal bivariate Birkhoff interpolation schemes and Pell’s equation, joint with N. <strong>Crainic</strong>,<br />
Commentationes Mathematicae Universitatis Carolinae, 50 (2009) 265-272.<br />
[32] Birkhoff interp. with rectang. sets of nodes and with few deriv., joint with N.<strong>Crainic</strong>,<br />
East Journal on Approximations, 14 no 4 (2008), pp. 423-437.<br />
[33] A On two-primary algebraic K-theory of quadratic number rings with focus on K 2 , joint<br />
work with Paul Ostvaer,<br />
Acta Arithemtica 87 (1999), pp. 223–243<br />
[34] A note on the denseness of complete invariant metrics, joint work with V. Csaba,<br />
Publ. Math. Debrecen 51 (1997), pp. 265–271<br />
29
Work in progress<br />
[1] Poisson manifolds of compact type I, joint work with D.M. Torres and R.L. Fernandes.<br />
[2] Poisson manifolds of compact type II, joint work with D.M. Torres and R.L. Fernandes.<br />
[3] Poisson manifolds of compact type III, joint work with D.M. Torres and R.L. Fernandes.<br />
[4] Normal <strong>for</strong>ms <strong>for</strong> symplectic foliations, joint work with I. Marcut.<br />
[5] De<strong>for</strong>mations in Lie algebra theory revisited, joint work with I. Struchiner and F. Schaetz.<br />
[6] The Geometry of Lie brackets (book in progress), joint work with R.L. Fernandes.<br />
30