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 combinatoire

Collection 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 combinatoire

Organisateur(s) Cassaigne, Julien ; Ferenczi, Sébastien ; Hubert, Pascal ; Kulaga-Przymus, Joanna ; Lemanczyk, Marius

Date(s) 12/12/2016 - 16/12/2016

URL associée https://www.chairejeanmorlet.com/1553.html

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Chapitres

Integral points on Markoff type cubic surfaces and dynamics

De Peter Sarnak

Apparaît également dans la collection : Exposés de recherche

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.

Informations sur la vidéo

Date de captation 12/12/2016
Date de publication 06/01/2017
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19100603
Citer cette vidéo Sarnak, Peter (12/12/2016). Integral points on Markoff type cubic surfaces and dynamics. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19100603
URL https://dx.doi.org/10.24350/CIRM.V.19100603

Domaine(s)

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