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Discrete Groups and Geometric Structures

Ziel

Discrete subgroups of Lie groups, whose study originated in Fuchsian differential equations and crystallography at the end of the 19th century, are the basis of a large aspect of modern geometry. They are the object of fundamental theories such as Teichmüller theory, Kleinian groups, rigidity theories for lattices, homogeneous dynamics, and most recently Higher Teichmüller theory. They are closely related to the notion of a geometric structure on a manifold, which has played a crucial role in geometry since Thurston. In summary, discrete subgroups are a meeting point of geometry with Lie theory, differential equations, complex analysis, ergodic theory, representation theory, algebraic geometry, number theory, and mathematical physics, and these fascinating interactions make the subject extremely rich.

In real rank one, important classes of discrete subgroups of semisimple Lie groups are known for their good geometric, topological, and dynamical properties, such as convex cocompact or geometrically finite subgroups. In higher real rank, discrete groups beyond lattices remain quite mysterious. The goal of the project is to work towards a classification of discrete subgroups of semisimple Lie groups in higher real rank, from two complementary points of view. The first is actions on Riemannian symmetric spaces and their boundaries: important recent developments, in particular in the theory of Anosov representations, give hope to identify a number of meaningful classes of discrete groups which generalise in various ways the notions of convex cocompactness and geometric finiteness. The second point of view is actions on pseudo-Riemannian symmetric spaces: some very interesting geometric examples are now well understood, and recent links with the first point of view give hope to transfer progress from one side to the other. We expect powerful applications, both to the construction of proper actions on affine spaces and to the spectral theory of pseudo-Riemannian manifolds

Finanzierungsplan

ERC-STG - Starting Grant

Gastgebende Einrichtung

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Netto-EU-Beitrag
€ 1 049 182,00
Adresse
RUE MICHEL ANGE 3
75794 Paris
Frankreich

Auf der Karte ansehen

Region
Ile-de-France Ile-de-France Paris
Aktivitätstyp
Research Organisations
Links
Gesamtkosten
€ 1 049 182,00

Begünstigte (1)