ESI 2007

Poisson sigma models, Lie algebroids, deformations, and higher analogues

Erwin Schrödinger Institute, August - September 2007

Organizers: Thomas Strobl (Lyon), Henrique Bursztyn (Rio de Janeiro), Harald Grosse (Vienna)


Poisson sigma models (PSMs) were originally introduced by Schaller, Strobl and Ikeda so as to unify several two-dimensional models of gravity and to cast them into a common form with Yang-Mills theories. PSMs are 2d topological field theories whose target geometry is given by Poisson structures. In the course of time, it has become clear that PSMs can be used in various ways as a fruitful source of mathematical insight, serving as a link between many central questions in mathematics. For example, as shown by Cattaneo and Felder, the perturbative quantization of the PSM recovers Kontsevich's famous solution to the long standing problem of deformation quantization of Poisson manifolds, whereas the reduced phase space of the PSM provides a universal model for a symplectic groupoid integrating the target Poisson manifold. The PSM construction of symplectic groupoids is intimately related to the solution of another classical problem in geometry: the explicit description of integrability conditions , due to Crainic and Fernandes, allowing Lie algebroids to be integrated to Lie groupoids.

Further investigations of sigma models are likely to lead to new contributions to mathematics. In this context, interesting sigma models have been recently considered, including several two-dimensional models related to "generalized geometries" and the "Courant sigma model" in three dimensions, which generalizes the Chern-Simons gauge theory. In another direction, the reformulation of 2d supergravity-Yang-Mills theories as PSMs with a super Poisson target may indicate connections between physical supergravity theories in higher dimensions and hidden algebroid type target geometries. In the general study of sigma models, there is a fundamental interplay between mathematics and physics: on the one hand, mathematical structures are a key element in the formulation of new physical theories, and such theories, on the other hand, may put known mathematical objects into a new perspective or bring to light new ones.

This program at the Erwin Schrödinger Institute (ESI) will be devoted to topics in mathematics and physics inspired by the Poisson sigma model and related models of geometric origin, bringing together leading mathematicians and mathematical physicists from various related directions. Topics to be covered include:

A list of invited participants can be found here. Click here for information on the period of visit of each participant.


The program will host various activities focusing on different aspects of the main theme. On top of regular research talks given by visitors, we plan to have introductory lectures/mini-courses on selected topics according to the following schedule:


Click here for the abstracts.

Extended lectures

These consist of two one-hour lectures.

There may be other extended lectures with precise dates to be announced. The information here will be constantly updated.

Daily schedule of seminars and lectures

The program will host a special workshop as well:

Workshop on Poisson geometry and sigma models

August 20 - 24, 2007

Organizers: Anton Alekseev, Henrique Bursztyn, Thomas Strobl

The workshop is partially supported by MISGAM (Methods of Integrable Systems, Geometry, Applied Mathematics), a scientific programme of the European Science Foundation .

Invited speakers:

The available abstracts can be found here . Click here for the schedule.

Please note that the minicourse of S. Merkulov, Poisson structure as a graph complex (see above), will start in the last day of the Workshop (Friday, August 24), and end on Saturday, August 25.

For more information about the workshop and possibilities of financial support, please contact the organizers.

Last modified on July 8, 2007