Objective
In this project, we propose to study mixing and rigidity properties of a large class of
flows in geometry and dynamical systems using novel microlocal and spectral methods.
Such methods, recently developed for flows with hyperbolicity, are based on the construction of
new functional spaces, adapted to the considered flow, on which the generating vector field is Fredholm with
discrete spectrum, known as the resonance spectrum. We want to apply these tools to the following categories of long-standing problems:
1) Geometric inverse problems: boundary and lens rigidity problems, analysis of the X-ray transforms for geodesic flows and its applications to Calderon and Gelfand inverse problems.
2) Rigidity for Anosov flows: determination of the minimal regularity of the stable/unstable foliations providing rigidity,
rigidity questions for regular conjugacies of flows.
3) Rate of mixing for flows of hyperbolic type: decay of correlations of Axiom A flows, Anosov flows, and
their compact Lie groups extensions, frame flows of negatively curved manifolds.
4) Resonances for locally symmetric spaces: relation between resonances of the flow and the spectrum of Laplacians on bundles.
To address these problems, we will develop a thorough analysis for the regularity and the long time properties of solutions to transport equations. We are convinced that the proposed approach will provide solutions to these problems, which have been out of reach for a long time.
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 applied mathematics dynamical systems
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics algebra algebraic geometry
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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.
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H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
MAIN PROGRAMME
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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-COG - Consolidator Grant
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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-COG
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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.