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Nombre de programmes trouvés : 29
Cours magistraux

le (1h32m17s)

Jean-Pierre Demailly - Kobayashi pseudo-metrics, entire curves and hyperbolicity of algebraic varieties (Part 1)

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.
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Cours magistraux

le (1h31m8s)

Dominique Cerveau - Holomorphic foliations of codimension one, elementary theory (Part 2)

In this introductory course I will present the basic notions, both local and global, using classical examples. I will explain statements in connection with the resolution of singularities with for instance the singular Frobenius Theorem or the Liouvilian integration. I will also present some open questions which I will motivate by examples. Dans ce cours introductif je m’attacherai à présenter les notions de base tant locales que globales au travers d’exemples classiques. J’aborderai des énoncés liés à la résolution des singularités avec par ...
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Cours magistraux

le (2h2m34s)

Jean-Pierre Demailly - Kobayashi pseudo-metrics, entire curves and hyperbolicity of algebraic varieties (Part 2)

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.
Voir la vidéo
Cours magistraux

le (1h30m54s)

Franc Forstnerič - Non singular holomorphic foliations on Stein manifolds (Part 2)

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 ...
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Cours magistraux

le (1h55m11s)

Dominique Cerveau - Holomorphic foliations of codimension one, elementary theory (Part 3)

In this introductory course I will present the basic notions, both local and global, using classical examples. I will explain statements in connection with the resolution of singularities with for instance the singular Frobenius Theorem or the Liouvilian integration. I will also present some open questions which I will motivate by examples. Dans ce cours introductif je m’attacherai à présenter les notions de base tant locales que globales au travers d’exemples classiques. J’aborderai des énoncés liés à la résolution des singularités avec par ...
Voir la vidéo
Cours magistraux

le (1h33m59s)

Jean-Pierre Demailly - Kobayashi pseudo-metrics, entire curves and hyperbolicity of algebraic varieties (Part 3)

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.  
Voir la vidéo
Cours magistraux

le (1h19m52s)

Franc Forstnerič - Non singular holomorphic foliations on Stein manifolds (Part 3)

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 ...
Voir la vidéo
Cours magistraux

le (1h24m43s)

Dominique Cerveau - Holomorphic foliations of codimension one, elementary theory (Part 4)

In this introductory course I will present the basic notions, both local and global, using classical examples. I will explain statements in connection with the resolution of singularities with for instance the singular Frobenius Theorem or the Liouvilian integration. I will also present some open questions which I will motivate by examples. Dans ce cours introductif je m’attacherai à présenter les notions de base tant locales que globales au travers d’exemples classiques. J’aborderai des énoncés liés à la résolution des singularités avec par exemple ...
Voir la vidéo
Cours magistraux

le (2h9m59s)

Jean-Pierre Demailly - Kobayashi pseudo-metrics, entire curves and hyperbolicity of algebraic varieties (Part 4)

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.  
Voir la vidéo
Cours magistraux

le (1h21m45s)

Serguei Ivachkovitch - Method of pseudoholomorphic curves and applications (Part 1)

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.
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