Objective
"The objective of this proposal is to study ""continuous"" (or C^0) objects, as well as C^0 properties of smooth objects, in the field of symplectic geometry and topology. C^0 symplectic geometry has seen spectacular progress in recent years, drawing attention of mathematicians from various background. The proposed study aims to discover new fascinating C^0 phenomena in symplectic geometry.
One circle of questions concerns symplectic and Hamiltonian homeomorphisms. Recent studies indicate that these objects possess both rigidity and flexibility, appearing in surprising and counter-intuitive ways. Our understanding of symplectic and Hamiltonian homeomorphisms is far from being satisfactory, and here we intend to study questions related to action of symplectic homeomorphisms on submanifolds. Some other questions are about Hamiltonian homeomorphisms in relation to the celebrated Arnold conjecture. The PI suggests to study spectral invariants of continuous Hamiltonian flows, which allow to formulate the C^0 Arnold conjecture in higher dimensions. Another central problem that the PI will work on is the C^0 flux conjecture.
A second circle of questions is about the Poisson bracket operator, and its functional-theoretic properties. The first question concerns the lower bound for the Poisson bracket invariant of a cover, conjectured by L. Polterovich who indicated relations between this problem and quantum mechanics. Another direction aims to study the C^0 rigidity versus flexibility of the L_p norm of the Poisson bracket. Despite a recent progress in dimension two showing rigidity, very little is known in higher dimensions. The PI proposes to use combination of tools from topology and from hard analysis in order to address this question, whose solution will be a big step towards understanding functional-theoretic properties of the Poisson bracket operator."
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 quantum physics
- natural sciences mathematics pure mathematics topology symplectic topology
- 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.
69978 Tel Aviv
Israel
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.