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

Organizer(s) Cassaigne, Julien ; Ferenczi, Sébastien ; Hubert, Pascal ; Kulaga-Przymus, Joanna ; Lemanczyk, Marius
Date(s) 12/12/2016 - 16/12/2016
linked URL https://www.chairejeanmorlet.com/1553.html
00:00:00 / 00:00:00
3 5

Integral points on Markoff type cubic surfaces and dynamics

By Peter Sarnak

Also appears in 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.

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Citation data

  • DOI 10.24350/CIRM.V.19100603
  • Cite this video 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

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