Objective
This project focuses on questions related to the deformation theory of algebraic structures in the very general setting of algebras over a prop (which includes various kinds of algebras and bialgebras). In particular, it aims to understand realizations of an algebraic structure at the (co)homology level in an algebraic structure up to homotopy at the (co)chain level. When this complex is of topological or geometric nature (e.g. the de Rham complex of a manifold), one expects to extract from these realizations new topological and geometric invariants. These realizations are not understood at present in various cases where bialgebra structures play a crucial role, especially with Poincaré duality, String topology and Deformation quantization. We use methods relying in particular on Quillen’s work on homotopical algebra, Lurie's higher category theory and Toen-Vezzosi’s derived algebraic geometry. We define and study the homotopy type of realization spaces of algebraic structures and develop a derived geometry approach to deformation theory of such structures. This machinery is set up to address three kinds of problems related to topology, geometry and mathematical physics. The first one is to use realization spaces of Poincaré duality structures and equivariant string topology to build new topological and geometric invariants of manifolds, solve an open problem of Sullivan about the realisation of known geometric invariants and understand the action of the Grothendieck-Teichmüller group on such structures. The second one is to use a derived geometry approach to these moduli spaces to compare deformation theories of bialgebras and algebras over the little disks operad and solve a longstanding formality conjecture of Kontsevich. The third one is to use deformation quantization of moduli stacks of algebraic structures up to homotopy to perform a far reaching generalization of Turaev's work to the construction of link invariants in higher dimensional manifolds.
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 mathematical physics
- natural sciences mathematics pure mathematics topology
- 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.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions
MAIN PROGRAMME
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H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
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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.
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)
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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) H2020-MSCA-IF-2015
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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.