The objectives of the proposal are;
1) to study the global regularization of pluri-sub-harmonic functions on almost complex manifolds, in a way that generalizes Demailly's regularization theorems for complex manifolds,
2) to improve the understanding of al most-analytic sets on almost complex and their singularities. It is likely that Siu's theorem on the analyticity of sublevel sets of closed positive currents can be extended to the almost complex case.
3) to introduce pseudo-holornorphic sub-schemes via non integrable (0, l)-connections on sheaves of smooth functions,
4) to prove that if the firs Chern class of a compact symplectic manifold verifies a certain positivity condition then the manifold is covered by pseudo-holomorhicrational curves,
5) to conclude the unsolved problem in the classification of the holonomy of Riemannian manifolds corresponding to Fano manifolds admitting a holomorphic contact structure - this is essentially the only case left from Berger's list which is riot fully understood.
The glob al plan work for the proposed project will be the following.
1) A during of 4 months for the study and the achievement of point 1.
2) A during of 6 months for the study and the achievement of point 5.
3) A during of 8 months for the study and the achievement of point 2.
4) A during of 2 months for acquirement of expertise concerning the point 3 and a during of 4 months for acquirement of expertise concerning the point 4.
5) During the reintegration period in France the applicant will spend 4 months for the execution of the point 3 and 8 months for the execution of the point 4.
Call for proposal
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