English
Integral points on Markoff type cubic surfaces and dynamics
Post-edited
Auteurs : Sarnak, Peter (Auteur de la conférence)
CIRM (Editeur )
11G05 - Elliptic curves over global fields
37A45 - Relations of ergodic theory with number theory and harmonic analysis
CIRM (Editeur )
Résumé :
Cubic surfaces in affine three space tend to have few integral points .However certain cubics such as $x^3 + y^3 + z^3 = m$, may have many such points but very little is known. We discuss these questions for Markoff type surfaces: $x^2 +y^2 +z^2 -x\cdot y\cdot z = m$ for which a (nonlinear) descent allows for a study. Specifically that of a Hasse Principle and strong approximation, together with "class numbers" and their averages for the corresponding nonlinear group of morphims of affine three space.
Codes MSC : 11G05 - Elliptic curves over global fields
37A45 - Relations of ergodic theory with number theory and harmonic analysis
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 06/01/17 Date de Captation : 12/12/16 Collection : Exposés de recherche Sous Collection : Research talks Catégorie arXiv : Number Theory ; Dynamical Systems Domaine(s) : Systèmes Dynamiques & EDO ; Théorie des Nombres Format : MP4 (.mp4) - HD Durée : 01:02:29 Audience : Chercheurs Download : https://videos.cirm-math.fr/2016-12-12_Sarnak.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : Jean-Morlet Chair: Ergodic theory and its connections with arithmetic and combinatorics / Chaire Jean Morlet : Théorie ergodique et ses connexions avec l'arithmétique et la combinatoireOrganisateurs de la Rencontre : Cassaigne, Julien ; Ferenczi, Sébastien ; Hubert, Pascal ; Kulaga-Przymus, Joanna ; Lemanczyk, Mariusz Dates : 12/12/16 - 16/12/16 Année de la rencontre : 2016 URL de la Rencontre : https://www.chairejeanmorlet.com/1553.html
Données de citation
DOI : 10.24350/CIRM.V.19100603Citer cette vidéo: Sarnak, Peter (2016). Integral points on Markoff type cubic surfaces and dynamics. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19100603 URI : http://dx.doi.org/10.24350/CIRM.V.19100603 |
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