Objective
Moduli spaces are spaces which describe all mathematical objects of some type. This proposal concerns the study of certain moduli spaces via techniques from homotopy theory, from several different points of view. The main moduli spaces in which we are interested are moduli spaces of manifolds, or equivalently classifying spaces of diffeomorphism groups of manifolds. We are also interested in spaces of positive scalar curvature metrics on smooth manifolds, which we study by relating them to moduli spaces of smooth manifolds.
The study of moduli spaces of manifolds via homotopy theory has seen a great deal of development in the last 20 years, the breakthrough result being Madsen and Weiss' calculation of the stable homology of moduli spaces of surfaces. More recently, Galatius and I have established analogous results for manifolds of higher dimension.
A main goal of this proposal is to study the homology of moduli spaces from a multiplicative point of view. This leads to higher-order forms of the phenomenon of homological stability in which the failure of ordinary homological stability is itself stable. Remarkably, our methods developed to handle moduli spaces of manifolds are sufficiently general to yield deep new results when applied to other moduli spaces in algebra and topology, such as moduli spaces of modules (equivalently, classifying spaces of general linear groups) or moduli spaces of graphs (equivalently, classifying spaces of automorphism groups of free groups). In each case our methods give new information about their homology outside of the traditional stable range.
Other goals of this proposal are to form new connections between spaces of Riemannian metrics of positive scalar curvature and infinite loop spaces, and to investigate the structure of tautological subrings of the cohomology of moduli spaces of manifolds, especially in relation to the tautological rings of moduli spaces of Riemann surfaces studied in algebraic geometry.
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 algebra
- natural sciences mathematics pure mathematics 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-STG - Starting 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-2017-STG
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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.
CB2 1TN CAMBRIDGE
United Kingdom
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.