English
Shrinking targets on homogeneous spaces and improving Dirichlet's Theorem
Multi angle
Auteurs : Kleinbock, Dmitry (Auteur de la Conférence)
CIRM (Editeur )
11J04 - Homogeneous approximation to one number
11J70 - Continued fractions and generalizations
22F30 - Homogeneous spaces
37A17 - Homogeneous flows
CIRM (Editeur )
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Résumé :
Optimal results on the improvements to Dirichlet's Theorem are obtained in the one-dimensional case. For simultaneous approximation the problem is open. I will describe reduction of the problem to dynamics both in one-dimensional case (via continued fractions) and for higher dimensions (via diagonal flows on the space of lattices). If time allows I'll mention an inhomogeneous version which is easier than the homogeneous one. Joint work with Nick Wadleigh.
Codes MSC : 11J04 - Homogeneous approximation to one number
11J70 - Continued fractions and generalizations
22F30 - Homogeneous spaces
37A17 - Homogeneous flows
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 15/02/17 Date de captation : 08/02/17 Sous collection : Research School arXiv category : Number Theory ; Dynamical Systems Domaine : Dynamical Systems & ODE ; Number Theory Format : MP4 (.mp4) - HD Durée : 01:05:27 Audience : Researchers ; Graduate Students Download : https://videos.cirm-math.fr/2017-02-08_Kleinbock.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Homogeneous spaces, diophantine approximation and stationary measures / Espaces homogenes. Approximation diophantienne. Mesures stationnairesOrganisateurs de la rencontre : Adamczewski, Boris ; Athreya, Jayadev ; Mercat, Paul ; Palesi, Frédéric Dates : 06/02/17 - 10/02/17 Année de la rencontre : 2017 URL Congrès : http://conferences.cirm-math.fr/1712.html
Données de citation
DOI : 10.24350/CIRM.V.19118903Citer cette vidéo: Kleinbock, Dmitry (2017). Shrinking targets on homogeneous spaces and improving Dirichlet's Theorem. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19118903 URI : http://dx.doi.org/10.24350/CIRM.V.19118903 |
Voir aussi
- [Multi angle] Counting and equidistribution of integral representations by quadratic norm forms in positive characteristic? / Auteur de la Conférence Paulin, Frédéric.
- [Multi angle] Dynamics on quotients of SL(2,C) by discrete subgroups - Lecture 2 / Auteur de la Conférence Schapira, Barbara.
- [Multi angle] Dynamics on homogeneous spaces and Diophantine approximation / Auteur de la Conférence Ghosh, Anish.
- [ Post-edited] Dense subgroups in simple groups - Lecture 2 / Auteur de la Conférence Benoist, Yves.
Bibliographie
- Kleinbock, D., & Wadleigh, N. (2017). A zero-one Law for improvements to Dirichlet's Theorem.
