Project description
Advancing the study of geometric structures
The study of geometric structures on manifolds, significantly influenced by Klein’s Erlangen Programme from 1872, has seen great advancements and extensive applications in geometric topology. Moreover, it has profound connections with several fields, including low-dimensional topology, differential geometry, complex geometry, and representation theory. The ERC-funded GENERATE project aims to make significant progress in pseudo-Riemannian-type geometric structures by adopting a novel approach that integrates geometric and analytic techniques. The project also seeks to achieve four interconnected objectives that are critical to its research. Finally, its findings and methodologies are expected to foster further developments in the field.
Objective
The study of geometric structures on manifolds finds its inspiration in Klein’s Erlangen Program from 1872, and has seen spectacular developments and applications in geometric topology since the work of Thurston at the end of the 20th century. Geometric structures lie at the crossroads of several disciplines, such as differential and algebraic geometry, low-dimensional topology, representation theory, number theory, real and complex analysis, which makes the subject extremely rich and fascinating.
In the context of geometric structures of pseudo-Riemannian type, the study of submanifolds with special curvature conditions has been very effective and led to some fundamental questions, such as the open conjectures of Andrews and Thurston from the 2000s, and the recently settled Labourie’s Conjecture. This project aims to obtain important results in this direction, towards four interconnected goals:
1. the study of quasi-Fuchsian hyperbolic manifolds, in particular leading to the proof of a strong statement that would imply the solution of the conjectures of Andrews and Thurston;
2. the achievement of curvature estimates of L^2-type on surfaces in Anti-de Sitter space;
3. the construction of metrics of (para)-hyperKähler type on deformation spaces of (G,X)-structures, and the investigation of their properties;
4. the study of existence and uniqueness of special submanifolds of dimension greater than 2 in pseudo-Riemannian symmetric spaces.
The project adopts an innovative approach integrating geometric and analytic techniques, and the results will have remarkable applications for Teichmüller theory and Anosov representations.
In the long term, the proposed methodology and the expected results will lead to further developments in various related directions, for instance: the study of pseudo-Riemannian manifolds of variable negative curvature, of higher dimensional pseudo-hyperbolic manifolds, and the deformation spaces of other types of (G,X)-structures.
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 topology
- natural sciences mathematics pure mathematics 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.
-
HORIZON.1.1 - 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.
HORIZON-ERC - HORIZON ERC Grants
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-2023-COG
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.
10124 Torino
Italy
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.