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Integral points on Markoff type cubic surfaces and dynamics
Post-edited
Authors : Sarnak, Peter (Author of the conference)
CIRM (Publisher )
11G05 - Elliptic curves over global fields
37A45 - Relations of ergodic theory with number theory and harmonic analysis
CIRM (Publisher )
Abstract :
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.
MSC Codes : 11G05 - Elliptic curves over global fields
37A45 - Relations of ergodic theory with number theory and harmonic analysis
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 06/01/17 Conference Date : 12/12/16 Subseries : Research talks arXiv category : Number Theory ; Dynamical Systems Mathematical Area(s) : Dynamical Systems & ODE ; Number Theory Format : MP4 (.mp4) - HD Video Time : 01:02:29 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2016-12-12_Sarnak.mp4 
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Information on the Event
Event Title : 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 combinatoireEvent Organizers : Cassaigne, Julien ; Ferenczi, Sébastien ; Hubert, Pascal ; Kulaga-Przymus, Joanna ; Lemanczyk, Mariusz Dates : 12/12/16 - 16/12/16 Event Year : 2016 Event URL : https://www.chairejeanmorlet.com/1553.html
Citation Data
DOI : 10.24350/CIRM.V.19100603Cite this video as: 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 |
See Also
- [Post-edited] Interview at CIRM: Peter Sarnak / Interviewee Sarnak, Peter.
- [Multi angle] The unsolved problems of Halmos / Author of the conference Weiss, Benjamin.
- [Multi angle] Primes with missing digits / Author of the conference Maynard, James.
- [Multi angle] The diameter of the symmetric group: ideas and tools / Author of the conference Helfgott, Harald.
- [Multi angle] Ergodicity of the Liouville system implies the Chowla conjecture / Author of the conference Frantzikinakis, Nikos.
- [Multi angle] Möbius randomness and dynamics six years later / Author of the conference Sarnak, Peter.
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