About Us

Our interests

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Welcome to the “Geometric structures” group of Utrecht University. Previously known as the “Poisson Geometry group”, we find “geometric structures” as a more faithful description of the interests of our group (although we do keep the name “Friday Fish seminar” for our Friday activities). Indeed, our interests are in the study of various geometric structures, such as:

- Poisson structures; generalized complex structures (and variations),
- Symplectic and contact structures (and variations),
- Foliations; equivariant geometry (group actions),
- Lie theory and the theory of Lie groupoids and algebroids,
- The general theory of G-structures.
- Cartan geometries (and Lie pseudogroups as symmetries)

What we do

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We study such structures from a differential geometric or topological point of view such as:

- Understand the interaction between the geometry of such structures and the topology of the underlying spaces, with the mind at “topological obstructions” to their existence,
- Build “geometric invariants” to distinguish such structures,
- Study local models for such structures, with the mind at “local form theorems”,
- Develop surgery constructions that allow one to build new interesting examples (often using the local models as building pieces), with the mind at “existence results”.
- Therefore construct new interesting examples, with the mind at “classification results”.
- Understand the possible deformations of such structures. Which ones are rigid?
- Understand the symmetries of such structures (both global and infinitesimal).
- Understand the interaction (and the bridges) between the various types of structures.
- Understand the dynamics of structure preserving maps, for example their (leafwise) fixed points.
- Find obstructions for structure preserving embeddings.

We use tools that come from differential geometry and topology, algebraic topology and analysis. We are also interested in the applications (or just the relevance) of such structures to various parts of Mathematical Physics and to the geometry of PDEs (partial differential equations). For more details, please see our web-pages.