Objective
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
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics mathematical analysis differential equations
- natural sciences mathematics pure mathematics mathematical analysis complex analysis
- natural sciences mathematics pure mathematics algebra algebraic geometry
You need to log in or register to use this function
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
-
H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
MAIN PROGRAMME
See all projects funded under this programme
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
ERC-STG - Starting Grant
See all projects funded under this funding scheme
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2016-STG
See all projects funded under this callHost institution
Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
75794 PARIS
France
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.