Objective
My proposal is to investigate some new aspects of the geometry of complex manifolds, foliations by complex leaves and their deformations. Emphasis is put on the relations between these three themes.
The basic objects of complex geometry are compact complex manifolds. However, only very special classes are well understood. And the only theory which applies to the general case is Kodaira-Spencer theory of deformations. To each structure of a compact complex manifold it associates a finite-dimensional space, called Kuranishi space, containing all the small deformations of this initial structure. Although it is a very classical theory, almost nothing is known about the geometry of this space. Last year, I discovered that it has a natural foliated structure and I want to study it more thoroughly.
On the other hand, Kuranishi spaces exist for transversely holomorphic foliations, which form a generalization of complex structures. There is however another natural generalization, that of foliation by complex leaves. Now in this case there is no Kuranishi space (the finite-dimensionality fails). I have some precise ideas to construct (finite-dimensional) Kuranishi spaces in a generalized sense.
Finally I also want to introduce a notion of geometric rigidity, which is better adapted to the case of a foliation than the classical notion of rigidity.
As a researcher, I work for twelve years on the geometry and topology of compact complex manifolds. But to achieve these goals, I need to strengthen my training in deformation theory. So I plan to spend two years at CRM, Barcelona, under the guidance of Marcel Nicolau, an expert in deformations of complex manifolds and transversely holomorphic foliations. I could also benefit from the intense mathematical activity of the CRM, especially in complex analysis and geometry.
Achieving these goals would open new lines of research and qualify me as a leading expert in the field. Last but not least, I could look for another position.
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 geometry
- natural sciences mathematics pure mathematics mathematical analysis complex analysis
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Programme(s)
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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
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP7-PEOPLE-2010-IEF
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Funding Scheme
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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
08193 Bellaterra
Spain
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