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Franc Forstnerič - Non singular holomorphic foliations on Stein manifolds (Part 1)
/ Fanny Bastien
/ 19-06-2012
/ Canal-u.fr
Forstnerič Franc
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Voir le résumé
A nonsingular holomorphic foliation of codimension on a complex manifold is locally given by the level sets of a holomorphic submersion to the Euclidean space . If
is a Stein manifold, there also exist plenty of global foliations of
this form, so long as there are no topological obstructions. More
precisely, if then any -tuple of pointwise linearly independent (1,0)-forms can be continuously deformed to a -tuple of differentials where is a holomorphic submersion of to . Such a submersion always exists if is no more than the integer part of . More generally, if is a complex vector subbundle of the tangent bundle such that is a flat bundle, then is homotopic (through complex vector subbundles of ) to an integrable subbundle, i.e., to the tangent bundle of a nonsingular holomorphic foliation on .
I will prove these results and discuss open problems, the most
interesting one of them being related to a conjecture of Bogomolov. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, courbes, institut fourier, summer school, feuilletages, holomorphic foliations
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Franc Forstnerič - Non singular holomorphic foliations on Stein manifolds (Part 3)
/ Fanny Bastien
/ Canal-u.fr
Voir le résumé
Voir le résumé
A nonsingular holomorphic foliation of codimension on a complex manifold is locally given by the level sets of a holomorphic submersion to the Euclidean space . If
is a Stein manifold, there also exist plenty of global foliations of
this form, so long as there are no topological obstructions. More
precisely, if then any -tuple of pointwise linearly independent (1,0)-forms can be continuously deformed to a -tuple of differentials where is a holomorphic submersion of to . Such a submersion always exists if is no more than the integer part of . More generally, if is a complex vector subbundle of the tangent bundle such that is a flat bundle, then is homotopic (through complex vector subbundles of ) to an integrable subbundle, i.e., to the tangent bundle of a nonsingular holomorphic foliation on .
I will prove these results and discuss open problems, the most
interesting one of them being related to a conjecture of Bogomolov. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, applications, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES
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François Lalonde - Applications of Quantum homology to Symplectic Topology (Part 1)
/ Fanny Bastien
/ 03-07-2012
/ Canal-u.fr
Lalonde François
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Voir le résumé
The
first two lectures will present the fundamental results of symplectic
topology : basic definitions, Moser’s lemma, normal forms of the
symplectic structure near symplectic and Lagrangian submanifolds,
characterization of Hamiltonian fibrations over any CW-complex. The
third course will give the application of quantum homology to the
splitting of the rational cohomology ring of any Hamiltonian fibration
over S2, a generalization of a result of Deligne in the algebraic case
and of Kirwan in the toric case. The fourth course will give the
application of the quantum homology of a Lagrangian submanifold to the
proof of the triviality of the monodromy of a weakly exact Lagrangian
submanifold in any symplectic manifold. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES
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Jean-Pierre Demailly - Kobayashi pseudo-metrics, entire curves and hyperbolicity of algebraic varieties (Part 2)
/ Fanny Bastien
/ Canal-u.fr
Voir le résumé
Voir le résumé
We
will first introduce the basic concepts pertaining to Kobayashi
pseudo-distances and hyperbolic complex spaces, including Brody’s
theorem and the Ahlfors-Schwarz lemma. One of the main goals of the
theory is to understand conditions under which a given algebraic variety
is Kobayashi hyperbolic. This leads to the introduction of jet spaces
and jet metrics, and provides a strong link between the existence of
entire curves and the existence of global algebraic differential
equations. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES
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Jean-Pierre Demailly - Kobayashi pseudo-metrics, entire curves and hyperbolicity of algebraic varieties (Part 3)
/ Fanny Bastien
/ Canal-u.fr
Voir le résumé
Voir le résumé
We
will first introduce the basic concepts pertaining to Kobayashi
pseudo-distances and hyperbolic complex spaces, including Brody’s
theorem and the Ahlfors-Schwarz lemma. One of the main goals of the
theory is to understand conditions under which a given algebraic variety
is Kobayashi hyperbolic. This leads to the introduction of jet spaces
and jet metrics, and provides a strong link between the existence of
entire curves and the existence of global algebraic differential
equations.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES
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Jean-Pierre Demailly - Kobayashi pseudo-metrics, entire curves and hyperbolicity of algebraic varieties (Part 4)
/ Fanny Bastien
/ Canal-u.fr
Voir le résumé
Voir le résumé
We
will first introduce the basic concepts pertaining to Kobayashi
pseudo-distances and hyperbolic complex spaces, including Brody’s
theorem and the Ahlfors-Schwarz lemma. One of the main goals of the
theory is to understand conditions under which a given algebraic variety
is Kobayashi hyperbolic. This leads to the introduction of jet spaces
and jet metrics, and provides a strong link between the existence of
entire curves and the existence of global algebraic differential
equations.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES
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Julien Duval - Kobayashi pseudo-metrics, entire curves and hyperbolicity of algebraic varieties 1/2
/ Fanny Bastien
/ 28-06-2012
/ Canal-u.fr
Duval Julien
Voir le résumé
Voir le résumé
indisponible Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES
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Julien Duval - Kobayashi pseudo-metrics, entire curves and hyperbolicity of algebraic varieties 2/2
/ Fanny Bastien
/ 29-06-2012
/ Canal-u.fr
Duval Julien
Voir le résumé
Voir le résumé
indisponible Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES
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Serguei Ivachkovitch - Method of pseudoholomorphic curves and applications (Part 3)
/ Fanny Bastien
/ 28-06-2012
/ Canal-u.fr
Ivachkovitch Serguei
Voir le résumé
Voir le résumé
The method of « pseudoholomorphic » curves proved itself to be extremely useful in different fields. In symplectic topology, for instance Gromov’s Nonsqueezing Theorem, Arnold’s conjecture and the Floer homology, the Gromov-Witten invariants. In complex analysis and geometry, for instane polynomial hulls of totally real surfaces, envelopes of meromorphy, holomorphic foliations. We shall develop the theory of complex curves in almost complex manifolds and discuss some of these applications in our lectures. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES
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