Objective
This proposal concerns the application of homotopy theoretic methods to multiple questions of geometric nature, and in particular the study of moduli spaces. Firmly based in topology, the research proposed here is strongly motivated by applications and potential applications to differential geometry, algebraic geometry and especially number theory.
Any “moduli space” parametrizes how certain objects may vary in families. The moduli spaces of manifolds parametrize how smooth manifolds may vary in families (smooth fiber bundles), and the representation varieties studied in the second major component parametrize how linear representations of a group may vary in algebraic families.
The homotopy theoretic study of moduli spaces of manifolds has seen spectacular successes in the last 15 years, kickstarted by a theorem of Madsen and Weiss concerning the topology of moduli spaces of 2-dimensional manifolds. Very recently, anongoing collaboration between O. Randal-Williams and myself promises to establish analoguous results for manifolds of higher dimension. If funded, the research proposed here will bring this research program to a point where all major results about surface moduli spaces have proven analogues for manifolds of higher dimension.
The second major component of this proposal has strong number-theoretic origins, but is essentially homotopy theoretic. It concerns the study of universal deformations of representations of (Galois) groups. If funded, the research in this component of the proposal, joint with Akshay Venkatesh, will develop derived (simplicial) deformation rings. Classical deformation rings have had spectacular applications in number theory (starting with Wiles’ work) and we also propose to begin the study of applications ofderived deformation rings.
Finally, the proposal contains smaller or more speculative projects, and points out many questions which might be suitable for the Ph.D.-students and postdocs also applied for in this proposal.
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 physical sciences relativistic mechanics
- natural sciences mathematics pure mathematics topology
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics arithmetics prime numbers
- natural sciences mathematics pure mathematics algebra algebraic geometry
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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-2015-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.
1165 KOBENHAVN
Denmark
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.