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DiGGeS SIGNED

Discrete Groups and Geometric Structures

Total Cost €

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EC-Contrib. €

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Partnership

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Project "DiGGeS" data sheet

The following table provides information about the project.

Coordinator
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS 

Organization address
address: RUE MICHEL ANGE 3
city: PARIS
postcode: 75794
website: www.cnrs.fr

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country France [FR]
 Total cost 1˙049˙182 €
 EC max contribution 1˙049˙182 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-STG
 Funding Scheme ERC-STG
 Starting year 2017
 Duration (year-month-day) from 2017-09-01   to  2022-08-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS FR (PARIS) coordinator 1˙049˙182.00

Map

 Project 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

 Publications

year authors and title journal last update
List of publications.
2019 Zhu, Feng
Relatively dominated representations
published pages: , ISSN: , DOI:
2020-04-15
2020 Glorieux, Olivier
Random path in negatively curved manifolds
published pages: , ISSN: , DOI:
2020-04-15
2020 Glorieux, Olivier; Yarmola, Andrew
Random triangles on flat tori
published pages: , ISSN: , DOI:
2020-04-15
2019 Burelle, Jean-Philippe
Rigidity of diagonally embedded triangle groups
published pages: , ISSN: , DOI:
2020-04-01
2018 Stecker, Florian
Balanced ideals and domains of discontinuity of Anosov representations
published pages: , ISSN: , DOI:
2020-04-01
2020 Danciger, Jeffrey; Guéritaud, François; Kassel, Fanny
Proper affine actions for right-angled Coxeter groups
published pages: , ISSN: 0012-7094, DOI:
Duke Mathematical Journal, to appear 2020-04-01
2018 Glorieux, Olivier; Monclair, Daniel; Tholozan, Nicolas
Hausdorff dimension of limit sets for projective Anosov representations
published pages: , ISSN: , DOI:
https://hal.archives-ouvertes.fr/hal-02419949 2020-04-01
2020 Kassel, Fanny; Kobayashi, Toshiyuki
Spectral analysis on pseudo-Riemannian locally symmetric spaces
published pages: , ISSN: , DOI:
2020-04-01
2019 Kassel, Fanny; Kobayashi, Toshiyuki
Spectral analysis on standard locally homogeneous spaces
published pages: , ISSN: , DOI:
2020-04-01
2020 Kassel, Fanny; Potrie, Rafael
Eigenvalue gaps for hyperbolic groups and semigroups
published pages: , ISSN: , DOI:
2020-04-01
2019 Glorieux, Olivier
The embedding of the space of negatively curved surfaces in geodesic currents
published pages: , ISSN: , DOI:
2020-04-01
2019 Burelle, Jean-Philippe; Francoeur, Dominik
Foliations between crooked planes in 3-dimensional Minkowski space
published pages: , ISSN: 0129-167X, DOI:
International Journal of Mathematics 30 2019-04-18
2019 Kassel, Fanny
Geometric structures and representations of discrete groups
published pages: 1113-1150, ISSN: , DOI:
Proceedings of the International Congress of Mathematicians 2018 (ICM 2018) 2019-04-18
2018 Danciger, Jeffrey; Guéritaud, François; Kassel, Fanny
Convex cocompact actions in real projective geometry
published pages: , ISSN: , DOI:
2019-04-18
2018 Kassel, Fanny; Kobayashi, Toshiyuki
Invariant differential operators on spherical homogeneous spaces with overgroups
published pages: , ISSN: , DOI:
2019-04-18
2018 Danciger, Jeffrey; Guéritaud, François; Kassel, Fanny
Convex cocompactness in pseudo-Riemannian hyperbolic spaces
published pages: 87-126, ISSN: 0046-5755, DOI:
Geometriae Dedicata \"192 (special issue \"\"Geomet 2019-04-18
2019 Glorieux, Olivier; Monclair, Daniel; Tholozan, Nicolas
Hausdorff dimension of limit sets for projective Anosov representations
published pages: , ISSN: , DOI:
2019-04-18
2018 Danciger, Jeffrey; Guéritaud, François; Kassel, Fanny
Proper affine actions for right-angled Coxeter groups
published pages: , ISSN: , DOI:
2019-04-18
2018 Burelle, Jean-Philippe; Treib, Nicolaus
Schottky presentations of positive representations
published pages: , ISSN: , DOI:
2019-04-18

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