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Jean-Pierre Demailly - Kobayashi pseudo-metrics, entire curves and hyperbolicity of algebraic varieties (Part 1)
/ Fanny Bastien
/ 18-06-2012
/ Canal-u.fr
Demailly Jean-Pierre
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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, 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
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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
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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
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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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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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Alexandre Sukhov - J-complex curves: some applications (Part 3)
/ Fanny Bastien
/ 27-06-2012
/ Canal-u.fr
Sukhov Alexandre
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Voir le résumé
We
will focus in our lectures on the following : 1. J-complex discs in
almost complex manifolds : general properties. Linearization and
compactness. Gromov’s method : the Fredholm alternative for the d-bar
operator. Attaching a complex disc to a Lagrangian manifold.
Application : exotic symplectic structures. Hulls of totally real
manifolds : Alexander’s theorem. 2. Real surfaces in (almost) complex
surfaces. Filling real 2-spheres by a Levi-flat hypersurface (Bedford
-Gaveau-Gromov theorem). Some applications. Symplectic and contact
structures. Reeb foliation and the Weinsten conjecture. Hofer’s proof of
the Weinstein conjecture. 3. J-complex lines and hyperbolicity. The KAM
theory and Moser’s stability theorem for entire J-complex curves in
tori. Global deformation and Bangert’s theorem. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES
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Alexandre Sukhov - J-complex curves: some applications (Part 4)
/ Fanny Bastien
/ 28-06-2012
/ Canal-u.fr
Sukhov Alexandre
Voir le résumé
Voir le résumé
We
will focus in our lectures on the following : 1. J-complex discs in
almost complex manifolds : general properties. Linearization and
compactness. Gromov’s method : the Fredholm alternative for the d-bar
operator. Attaching a complex disc to a Lagrangian manifold.
Application : exotic symplectic structures. Hulls of totally real
manifolds : Alexander’s theorem. 2. Real surfaces in (almost) complex
surfaces. Filling real 2-spheres by a Levi-flat hypersurface (Bedford
-Gaveau-Gromov theorem). Some applications. Symplectic and contact
structures. Reeb foliation and the Weinsten conjecture. Hofer’s proof of
the Weinstein conjecture. 3. J-complex lines and hyperbolicity. The KAM
theory and Moser’s stability theorem for entire J-complex curves in
tori. Global deformation and Bangert’s theorem. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES
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Andrei Teleman - Instantons and holomorphic curves on surfaces of class VII (Part 1)
/ Fanny Bastien
/ 02-07-2012
/ Canal-u.fr
Teleman Andrei
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Voir le résumé
This
series of lectures is dedicated to recent results concerning the
existence of holomorphic curves on the surfaces of class VII. The first
lecture will be an introduction to the Donaldson theory. We will present
the fundamental notions and some important results in the theory,
explaining ideas of the proofs. In the second lecture we will present
the theory of holomorphic fiber bundles on complex surfaces, the
stability notion, moduli spaces and the Kobayashi-Hitschin
correspondence that links moduli spaces of stable fiber bundles (defined
in the fram of complex geometry) to moduli spaces of instantons
(defined in the frame of the Donaldson theory). In the last two lectures
we will prove the existence of holomorphic curves on minimal surfaces
of class VII with b2=1 or 2 and we will present the general strategy and
the last results obtained in the general case. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES
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Andrei Teleman - Instantons and holomorphic curves on surfaces of class VII (Part 2)
/ Fanny Bastien
/ 03-07-2012
/ Canal-u.fr
Teleman Andrei
Voir le résumé
Voir le résumé
This
series of lectures is dedicated to recent results concerning the
existence of holomorphic curves on the surfaces of class VII. The first
lecture will be an introduction to the Donaldson theory. We will present
the fundamental notions and some important results in the theory,
explaining ideas of the proofs. In the second lecture we will present
the theory of holomorphic fiber bundles on complex surfaces, the
stability notion, moduli spaces and the Kobayashi-Hitschin
correspondence that links moduli spaces of stable fiber bundles (defined
in the fram of complex geometry) to moduli spaces of instantons
(defined in the frame of the Donaldson theory). In the last two lectures
we will prove the existence of holomorphic curves on minimal surfaces
of class VII with b2=1 or 2 and we will present the general strategy and
the last results obtained in the general case. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES
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Claude Viterbo - Théorie des faisceaux et Topologie symplectique (Part 1)
/ Fanny Bastien
/ 03-07-2012
/ Canal-u.fr
Viterbo Claude
Voir le résumé
Voir le résumé
L’utilisation
de méthodes de théorie des faisceaux (Kashiwara-Schapira)a été
dévelopée ces dernières années par Tamarkin, Nadler, Zaslow, Guillermou,
Kashiwara et Schapira. Nous essaierons d’en donner un aperçu à la fois
pour démontrer des résultats classiques, comme la conjecture d’Arnold,
et pour des résultats nouveaux.
The
use of methods from the Sheaf Theory (Kashiwara-Schapira) was
developped recently by Tamarkin, Nadler, Zaslow, Guillermou, Kashiwara
and Schapira. We will try to give an insight of that, in order to prove
classical results, such as the Arnold conjecture, and to obtain new
results.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES
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