Objective
We propose a program that aims at providing new developments and new applications of shifted symplectic and Poisson structures. It is formulated in the language and framework of derived algebraic geometry after Toën–Vezzosi and Lurie.
On the foundational side, we will introduce the new notion of shifted symplectic groupoids and prove that they provide an alternative approach to shifted Poisson structures (as they were defined by the PI together with Tony Pantev, Bertrand Toën, Michel Vaquié and Gabriele Vezzosi). Along the way, we shall be able to prove several conjectures that have recently been formulated by the PI and other people.
Applications are related to mathematical physics. For instance:
- we will provide an interpretation of the Batalin–Vilkovisky formalism in terms of derived symplectic reduction.
- we will show that the semi-classical topological field theories with values in derived Lagrangian correspondences that were previously introduced by the PI are actually fully extended topological field theories in the sense of Baez–Dolan and Lurie.
- we will explain how one may use this formalism to rigorously construct a 2D topological field theory that has been discovered by Moore and Tachikawa.
Quantization problems will also be discussed at the end of the proposal.
This project proposal lies at the crossroads of algebraic geometry, mathematical physics (in its algebraic and geometric aspects) and higher algebra.
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 symplectic 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.1.1. - 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-2017-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.
34090 Montpellier
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.