Objective
In this project I intend to substantially advance research in different fields in contemporary symplectic geometry. The project is articulated in five sections: A. Singular symplectic and Poisson reduction of cotangent bundles. I will focus in an unfinished topic in the theory of singular reduction: its application to cotangent bundles. I will study the fibered structure of the singular reduced spaces in the Poisson and symplectic cases. B. Singular reduction in generalized complex geometry. In the last two years we have seen a dramatic impulse of the theory of Hamiltonian actions and its reduction theory in generalized complex geometry. I will study the problem of the singular reduction of this geometry. This is a relevant problem that has remained untouched and which is expected to attract strong international scientific efforts in a near future. C. Reduction and groupoids. There is an increasing interest in the reduction theory of Hamiltonian groupoid actions and its relationship with Poisson geometry. I will study these topics in both the regular and singular settings. D. Local geometry of Hamiltonian actions. I will produce a normal form adapted to cotangent-lifted Hamiltonian actions analogous to the Marle-Guillemin-Sternberg normal form for arbitrary symplectic manifolds. This will reflect the original fibered geometry of the cotangent bundle and it will be applied to the study of the local properties of the spaces obtained in A., as well as to the investigation of the local dynamics of symmetric Hamiltonian systems (see E.). Also, I will investigate the existence of such normal forms in Poisson and generalized complex geometries. E. Bifurcations of relative equilibria in Hamiltonian systems. I will apply the results of D. to the qualitative study of the dynamics of Hamiltonian systems of mechanical type. Specifically, it is to be expected that the fibered geometry of the normal form obtained in D. will be crucial to the study of their bifurcations.
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 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.
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.
FP7-PEOPLE-2007-2-1-IEF
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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.
Coordinator
M13 9PL Manchester
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.