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Date
Editeur
Auteur
Titre
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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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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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Accéder à la ressource
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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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Accéder à la ressource
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Jean-Louis Verger-Gaugry - Limit Equidistribution (Part 2)
/ Fanny Bastien
/ Canal-u.fr
Voir le résumé
Voir le résumé
indisponible Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, dynamics, institut fourier, summer school, number theory
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Guy David - Minimal sets (Part 2)
/ Fanny Bastien
/ Canal-u.fr
Voir le résumé
Voir le résumé
indisponible Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
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Accéder à la ressource
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Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 3)
/ Fanny Bastien
/ Canal-u.fr
Voir le résumé
Voir le résumé
In these lectures I will first
recall the basic notions and results that are needed to study minimal
surfaces in the smooth setting (above all the area formula and the first
variation of the area), give a short review of the main (classical)
techniques for existence results, and then outline the theory of Finite
Perimeter Sets, including the
main results of the theory (compactness, structure of distributional
derivative, rectifiability). If time allows, I will conclude with a few
applications. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
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Accéder à la ressource
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Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 2)
/ Fanny Bastien
/ Canal-u.fr
Voir le résumé
Voir le résumé
In these lectures I will first
recall the basic notions and results that are needed to study minimal
surfaces in the smooth setting (above all the area formula and the first
variation of the area), give a short review of the main (classical)
techniques for existence results, and then outline the theory of Finite
Perimeter Sets, including the
main results of the theory (compactness, structure of distributional
derivative, rectifiability). If time allows, I will conclude with a few
applications. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
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Accéder à la ressource
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Franc Forstnerič - Non singular holomorphic foliations on Stein manifolds (Part 4)
/ 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) : Grenoble, école d'été, mathématiques, institut fourier, summer school, holomorphic foliations
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Accéder à la ressource
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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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Accéder à la ressource
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Franc Forstnerič - Non singular holomorphic foliations on Stein manifolds (Part 2)
/ 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, courbes, institut fourier, summer school, holomorphic foliations, COURBES PSEUDOHOLOMORPHES
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Accéder à la ressource
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