# Arbeitsgemeinschaft Poisson-Geometry

## Winter term 2014/2015

#### News

#### Preliminary Program

This "Arbeitsgemeinschaft" aims at students in the master
programs in
Mathematik
or in
Mathematische
Physik with interests in a currently very active topic in
differential geometry.

Poisson manifolds are smooth manifolds with the additional
structure of a Poisson bracket for the smooth
functions. Equivalently, this is the additional datum of a
Poisson tensor, an antisymmetric contravariant tensor field
satisfing a particular non-linear PDE, the Jacobi identity.

The course consists of essentially two components: first, a
lecture where the basic notions of Poisson geometry are
explained. The prelimiary program for the lecture component
includes the following topics:

- The Schouten bracket
- Poisson manifolds
- Hamiltonian and Poisson vector fields
- Exampes and constructions
- Symplectic foliation and splitting theorem
- Poisson maps
- Lie algebroids
- Poisson cohomology
- Modular and fundamental class
- Formal deformation of Poisson structures

The second component will be a seminar by the students on more
particular topics. Here we plan to have talks in the area of
Poisson-Lie groups and Lie bialgebras.

#### Prerequisites

We expect some good knowledge in differential geometry
(manifolds, tensor calculus, vector bundles), and some knowledge
in Lie theory (matrix Lie groups and Lie algebras) might be
useful.

#### Introductory literature

The list of references is quite
long, everyone should be able to find some favorites in here.

#### Dates (not yet fixed!)

- Thursday 10 - 12 in the seminar room S0.101 (BSZ) or SE31
(mathematical physics).
- The precise dates for the seminar talks will be fixed during
the semester. They will take place at the end of the semester.

#### Links

- On WueCampus there will be a
course
for this "Arbeitsgemeinschaft". As soon as this is enabled, it
will replace this homepage.

Impressum und Datenschutz