Summer School (July 23-27, 2012)
The Summer School on Poisson Geometry aims to introduce the participant to Poisson Geometry (and related fields), as well as to present some of the more recent developments, and open problems, in the field. The school targets students in their final years, PhD students, young researchers. Required background: basic differential geometry.
The school will take place in the city of Utrecht (the Netherlands), and is organized by the Poisson Geometry group of the Mathematics Department in Utrecht University with the help of the Summer School Organization of Utrecht University.
The school duration is one week consisting of 4 minicourses. The school will be followed by a week long conference. Registration to the school includes registration to the conference.
About Poisson Geometry
Poisson Geometry lies on the cross road of Mathematical Physics and Geometry. It originates in the mathematical formulation of Hamiltonian mechanics and as the semiclassical limit of quantum systems. Although Poisson structures can be traced back to some of the classical works of the 19th century (Poisson, Hamilton, Jacobi, Lie), Poisson Geometry started as a field around 1980 with the work of Lichnerowicz, Weinstein, etc. The field developed rapidly, stimulated by the connections with a large number of areas in mathematics and mathematical physics, including differential geometry and Lie theory, quantization, noncommutative geometry, representation theory and quantum groups, geometric mechanics, integrable systems, etc. Major developments took place especially over the last 15 years; some of the highlights are Kontsevich's formality theorem, the study of Poisson-sigma models and the relationship to the "integrability problem" for Lie algebroids, the connections with the moduli space of flat connections (and various moment map theories), singular reduction, connections with (generalized) complex geometry, etc.
Mathematically, Poisson Geometry is an amalgam of three classical theories: (it is) Foliation Theory (inside which) Symplectic Geometry and Lie Theory (interact with each other). Geometrically, a Poisson structure on a space M is, first of all, a (possibly singular) foliation of M; hence M is partitioned into leaves. Secondly, the leaves are endowed with symplectic structures. Thirdly, transversal to the leaves, we have Lie algebras. This interaction actually goes much deeper, once Lie groupoids are brought into the picture: the symmetries of Poisson structures are encoded in a Lie groupoid which is a symplectic manifold (a symplectic groupoid). Alltogether, one of the strengths of Poisson Geoemtry is its potential to provide (often unexpected) interplays between other such fields.