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Differential Geometry

Faculty of Sciences | Mathematics

(Code: ULB175)

Complex, symplectic and contact geometry, quantisation and interactions (ARC)

No funding agency referenced.

This research project involves three inter-linked subjects: quantisation, symplectic geometry and Kähler geometry. The research will follow two main  ...

Kahler Geometry

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Extremal Kähler metrics, when they exist, are ''canonical'' representatives of their Kähler class. Their existence is conjecturaly equiavlent to the  ...

Definite connections

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An SO(3)-connection on a 4-manifold is called definite if its curvature is non-zero on every tangent 2-plane. Given such a connection the corresponding ...

Complex geometry of flat bundles over hyperbolic 3-manifolds

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The frame bundle X of a hyperbolic 3-manifold M is naturally a complex manifold with trivial canonical bundle. From this it is possible to give a holom ...

Topological symplectic manifolds

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Study and comparison of different definitions of topological symplectic manifolds. Tentative constructions of examples.

Symplectic connections and symplectic geometry

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Study of symplectic connections having certain curvature properties or solutions of a variational principle. Links with symplectic reduction and with p ...

Deformation quantization of symplectic and Poisson manifolds

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Classification, group actions, homomorphisms,involutions,  representations.

Classes of homogeneous symplectic manifolds and of symplectic symmetric spaces

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Study of conformal actions for homogeneous symplectic manifolds and symplectic symmetric spaces.

Multi-dimensional Morse theory

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The central object is a map between manifolds. We consider the topological complexity both of the image and of the level sets of such maps as it can be ...