Objective
This project proposes new research directions that originate in the field of Poisson Geometry and which reach out towards other fields of Differential Geometry and Topology. It can also be seen as the development of a new field- Poisson Topology, the birth of which is clearly predicted by the recent results of the PI on stability of symplectic leaves.
Aims:
1. solving some of the most fundamental open problems in Poisson Geometry.
2. breaking the current boundaries of Poisson Geometry and bringing it at the forefront of the interplay between other fields in geometry (Foliation Theory, Symplectic Geometry etc).
Methods/tools:
1. build on the breakthrough results of the PI (and his collaborators) such as the one on the integrability of Lie algebroids or the geometric approach to Conn-Weinstein theorem.
2. new tools in Poisson Geometry such as Nonlinear Functional Analysis or the use of the fundamental ideas of Cartan that were not yet exploited in Poisson Geometry (G-structures, Exterior Differential Systems, etc ).
New directions: I propose several interacting directions/subprojects, each one of independent interest. For example:
- study of local invariants in Poisson Geometry (a wide-open problem) based on PI's work and the use of ideas from G-structures.
- a new unified approach to stability theories, such as Mather's theory or Nijenhuis-Richardson's
(apparently unrelated!). Poisson Geometry plays an unifying role. We expect new fundamental results in Poisson Topology and related fields (including moduli spaces of flat connections).
- the study of global aspects of Poisson Geometry. E.g. the existence of codimension one Poisson structures on spheres (the 5-dimensional sphere was settled only last year!). Recall that the similar problem in Foliation Theory served as a driving force for the field (and will be used here). Global aspects will also take us to the world of Symplectic Topology- a high risk/high return journey that has never been taken before
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: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
- natural sciences mathematics pure mathematics topology symplectic topology
- natural sciences mathematics pure mathematics mathematical analysis functional analysis
- natural sciences mathematics pure mathematics 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.
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.
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.
ERC-2011-StG_20101014
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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.
Host institution
3584 CS Utrecht
Netherlands
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.