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 Sous collection : Research talks arXiv category : Number Theory ; Dynamical Systems Domaine : Dynamical Systems & ODE ; Number Theory Format : MP4 (.mp4) - HD Durée : 01:02:29 Audience : Researchers 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 Congrès : 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 |
Voir aussi
- [ Post-edited] Interview at CIRM: Peter Sarnak / Personne interviewée Sarnak, Peter.
- [Multi angle] The unsolved problems of Halmos / Auteur de la Conférence Weiss, Benjamin.
- [Multi angle] Primes with missing digits / Auteur de la Conférence Maynard, James.
- [Multi angle] The diameter of the symmetric group: ideas and tools / Auteur de la Conférence Helfgott, Harald.
- [Multi angle] Ergodicity of the Liouville system implies the Chowla conjecture / Auteur de la Conférence Frantzikinakis, Nikos.
- [Multi angle] Möbius randomness and dynamics six years later / Auteur de la Conférence Sarnak, Peter.
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