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| Alexander Gorodnik - Diophantine approximation and flows on homogeneous spaces (Part 1) (en Anglais) | |||
Droits : CC BY-NC-ND 4.0 Auteur(s) : Gorodnik Alexander, Bastien Fanny 24-06-2013 Description : The fundamental problem in the theory of Diophantine approximation is to understand how well points in the Euclidean space can be approximated by rational vectors with given bounds on denominators. It turns out that Diophantine properties of points can be encoded using flows on homogeneous spaces, and in this course we explain how to use techniques from the theory of dynamical systems to address some of questions in Diophantine approximation. In particular, we give a dynamical proof of Khinchin’s theorem and discuss Sprindzuk’s question regarding Diophantine approximation with dependent quantities, which was solved using non-divergence properties of unipotent flows. In conclusion we explore the problem of Diophantine approximation on more general algebraic varieties. Mots-clés libres : mathématiques,Grenoble,école d'été,dynamics,institut fourier,summer school,number theory | TECHNIQUE Type : image en mouvement Format : video/x-flv Source(s) : rtmpt://fms2.cerimes.fr:80/vod/institut_fourier/alexander.gorodnik.diophantine.approximation.and.flows.on.homogeneous.spaces.part.1._22919/gorodnik_ecoleete_24062013_sd.mp4 | ||
Entrepôt d'origine : Canal-u.fr Identifiant : oai:canal-u.fr:22919 Type de ressource : Ressource documentaire | |||
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| Alexander Gorodnik - Diophantine approximation and flows on homogeneous spaces (Part 1) (en Anglais) | |||||||||
Identifiant de la fiche : 22919 Schéma de la métadonnée : LOMv1.0, LOMFRv1.0 Droits : libre de droits, gratuit Droits réservés à l'éditeur et aux auteurs. CC BY-NC-ND 4.0 Auteur(s) : GORODNIK ALEXANDER Éditeur(s) : Fanny Bastien 24-06-2013 Description : The fundamental problem in the theory of Diophantine approximation is to understand how well points in the Euclidean space can be approximated by rational vectors with given bounds on denominators. It turns out that Diophantine properties of points can be encoded using flows on homogeneous spaces, and in this course we explain how to use techniques from the theory of dynamical systems to address some of questions in Diophantine approximation. In particular, we give a dynamical proof of Khinchin’s theorem and discuss Sprindzuk’s question regarding Diophantine approximation with dependent quantities, which was solved using non-divergence properties of unipotent flows. In conclusion we explore the problem of Diophantine approximation on more general algebraic varieties. Mots-clés libres : mathématiques, Grenoble, école d'été, dynamics, institut fourier, summer school, number theory
| PEDAGOGIQUE Type pédagogique : cours / présentation Niveau : doctorat TECHNIQUE Type de contenu : image en mouvement Format : video/x-flv Taille : 2.84 Go Durée d'exécution : 1 heure 18 minutes 19 secondes RELATIONS Cette ressource fait partie de : | ||||||||
Entrepôt d'origine : Canal-u.fr Identifiant : oai:canal-u.fr:22919 Type de ressource : Ressource pédagogique | |||||||||
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