Our research ranges from the general (i.e. the development of abstract frameworks to tackle the study of geometric structures) to the specific (the study of concrete geometries). In doing so, we borrow tools from Algebra, Geometric Analysis, and Homotopy Theory. Some of our research interests include:
- Foliation Theory
- Generalised Geometry
- Geometry of PDEs
- Index Theory
- Lie Theory, including Lie algebroids and groupoids
- Non-linear elliptic PDEs and their applications in Differential Topology
- Poisson Geometry
- Symplectic Geometry and Topology, Contact Topology
- Subriemannian Geometry
Supervisor: Marius Crainic
Erik van den Ban (webpage)
Interests: Lie groups, symmetric spaces, harmonic analysis, representation theory, Radon transforms, differential geometry.
Gil Cavalcanti (webpage)
Interests: Differential geometry and differential topology of symplectic, complex and generalized complex manifolds as well as their applications to string theory.
Marius Crainic (webpage)
Interests: Differential Geometry - especially Poisson, but also Symplectic, Contact, generalised complex structures, Foliations, Lie groupoids (active), Lie pseudogroups, EDS and the geometry of PDEs (more recent), Noncommutative Geometry (dormant).
Supervisor: Álvaro del Pino
Interests: Differential Geometry and Topology, particularly the h-principle
Maarten Mol (webpage)
Supervisor: Marius Crainic
Álvaro del Pino Gómez (webpage)
Interests: Differential Geometry and Topology, particularly h-principle and topological aspects in the study and classification of geometric structures (some concrete examples: symplectic, contact, and Engel structures; other bracket-generating distributions).
Supervisor: Gil Cavalcanti & Marius Crainic
Fabian Ziltener (webpage)
Interests: Symplectic geometry, gauge theory, and partial differential equations.
Miniworkshop on Symplectic Geometry. This is a yearly event organised by O. Fabert (VU) and F. Ziltener (UU). The ninth edition took place in Utrecht in 2019.
Dutch Differential Topology and Geometry seminar. The DDT&G is a monthly seminar organised between the universities of Amsterdam, Leiden and Utrecht. It features 2-hour minicourses aimed at a broad audience of master students and researchers, and focused on exciting recent developments.
The Friday Fish. Our (formerly local) seminar on Poisson Geometry, now available online.
Higher Geometric Structures along the Lower Rhine. This is a biyearly event jointly organised between the universities of Bonn, Nijmegen and Utrecht. Its focus lies on the development and application of new structures in geometry and topology. The last workshop took place in 2020.
Teaching and supervision
We are involved in teaching and supervision at the bachelor, master, and PhDs levels. You can find more information, including relevant courses and potential thesis projects, in the following links:
- Differential Geometry in the Bachelor.
- Master track in Differential Geometry and Lie Theory.
- General information about the Master in Mathematical Sciences.
- Our PhD programme.