A volume edited by T Ratiu, A Weinstein and myself

Geometry and Topology Monographs, Vol 17 (2011)

http://msp.warwick.ac.uk/gtm/2011/17/

Editors: Tudor Ratiu, Alan Weinstein and Nguyen Tien Zung

Trieste

Poisson geometry is a rapidly growing subject,

with many interactions and applications in areas of mathematics

and physics, such as classical differential geometry, Lie theory,

noncommutative geometry, integrable systems, fluid dynamics, quantum

mechanics, and quantum field theory. Recognizing the role played by

Poisson geometry and the significant research it has generated, the

Abdus Salam International Centre for Theoretical Physics in Trieste,

Italy, sponsored a 3–week summer activity on this subject (July 4–22

2005) in order to bring it to the attention of scientists and students

from developing countries. There was an overwhelming response to this

program, which brought together more than 150 participants from all over

the world with varied backgrounds, from graduate students to experts.

The program consisted of a two-week intensive school

comprising 10 minicourses, followed by a week-long international research

conference. The lecturers at the school were asked to turn their notes

into sections of a book that could serve as a quick introduction to the

current state of research in Poisson geometry. We hope that the present

volume will be useful to people who want to learn about Poisson geometry

and its applications.

Geometry & Topology Monographs 17

(2011)

Contents

Lectures on integrability of Lie

brackets

1

Marius Crainic and Rui Fernandes

Normal forms of Poisson

structures

109

Jean-Paul Dufour and Tien Zung Nguyen

Deformation quantisation of

Poisson manifolds

171

Simone Gutt

Applications of Poisson geometry

to physical problems

221

Darryl D Holm

Hamiltonian and quantum

mechanics

385

Anatol Odzijewicz

Lectures on Poisson

groupoids

473

Camille Laurent-Gengoux, Mathieu Stiénon and Ping Xu

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