Project description
The geometry of Anosov representations under study
The EU-funded AnSur project aims to investigate the links between curves in flag manifolds, surface solutions of geometric partial differential equations in affine symmetric spaces and functions on the moduli space of curves. The research will be geared towards a general class of functions on moduli spaces of Anosov representations and uniformly hyperbolic bundles. The goal will be to identify a family of curves acting as potential asymptotic boundaries, similar to quasisymmetric curves in the sphere. Researchers will then prove the existence and uniqueness of surfaces bounded by these curves. Their areas will be considered at critical points on the moduli space and as a renormalising function to take into account the volumes of these spaces.
Objective
We propose to study links between curves in flag manifolds, surfaces solutions of geometric partial differential equations in some affine symmetric spaces, and functions on the moduli space of curves. We will consider the relevant energy functions on the moduli spaces of those curves, or on the moduli space of Anosov representations for periodic data, in particular in the context of positivity. Amongst our concrete ambitious goals are: obtain topological invariant through quantising Anosov deformation spaces, define and compute volumes of Anosov deformation spaces and prove recursion formulae for them, find surfaces in symmetric spaces associated to opers and the relevant higher-rank Liouville action, solve special cases of the Auslander conjecture using foliated spaces.
More specifically, the backbone of this project is to explore a general class of functions on moduli spaces of Anosov representations and, beyond, of uniformly hyperbolic bundles. Then, we propose to identify the family of curves that will be possible asymptotic boundaries -- in the spirit of quasisymmetric curves in the sphere -- the periodic ones corresponding to Anosov representations. We will prove the existence and uniqueness of surfaces bounded at infinity by these curves. Going back, we will consider the area of such a surface, both at critical points on the moduli space, and as a renormalising function allowing to consider volumes of these moduli spaces. Finally, we will consider the space foliated by surfaces solutions of the asymptotic datum, and define entropy.
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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HORIZON.1.1 - European Research Council (ERC)
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Topic(s)
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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
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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-2022-ADG
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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.
06100 Nice
France
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