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Counting and equidistribution of integral representations by quadratic norm forms in positive characteristic?
Multi angle
Authors : Paulin, Frédéric (Author of the conference)
CIRM (Publisher )
11J61 - Approximation in non-Archimedean valuations
20E08 - Groups acting on trees
20G25 - Linear algebraic groups over local fields and their integers
37A25 - Ergodicity, mixing, rates of mixing
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
CIRM (Publisher )
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Abstract :
In this talk, we will prove the projective equidistribution of integral representations by quadratic norm forms in positive characteristic, with error terms, and deduce asymptotic counting results of these representations. We use the ergodic theory of lattice actions on Bruhat-Tits trees, and in particular the exponential decay of correlation of the geodesic flow on trees for Hölder variables coming from symbolic dynamics techniques.
MSC Codes : 11J61 - Approximation in non-Archimedean valuations
20E08 - Groups acting on trees
20G25 - Linear algebraic groups over local fields and their integers
37A25 - Ergodicity, mixing, rates of mixing
37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 15/02/17 Conference Date : 09/02/17 Subseries : Research School arXiv category : Dynamical Systems ; Number Theory Mathematical Area(s) : Dynamical Systems & ODE ; Number Theory Format : MP4 (.mp4) - HD Video Time : 01:03:47 Targeted Audience : Researchers ; Graduate Students Download : https://videos.cirm-math.fr/2017-02-09_Paulin.mp4 
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Information on the Event
Event Title : Homogeneous spaces, diophantine approximation and stationary measures / Espaces homogenes. Approximation diophantienne. Mesures stationnairesEvent Organizers : Adamczewski, Boris ; Athreya, Jayadev ; Mercat, Paul ; Palesi, Frédéric Dates : 06/02/17 - 10/02/17 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1712.html
Citation Data
DOI : 10.24350/CIRM.V.19119103Cite this video as: Paulin, Frédéric (2017). Counting and equidistribution of integral representations by quadratic norm forms in positive characteristic?. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19119103 URI : http://dx.doi.org/10.24350/CIRM.V.19119103 |
See Also
- [Multi angle] Shrinking targets on homogeneous spaces and improving Dirichlet's Theorem / Author of the conference Kleinbock, Dmitry.
- [Multi angle] Dynamics on quotients of SL(2,C) by discrete subgroups - Lecture 2 / Author of the conference Schapira, Barbara.
- [Multi angle] Dynamics on homogeneous spaces and Diophantine approximation / Author of the conference Ghosh, Anish.
- [Post-edited] Dense subgroups in simple groups - Lecture 2 / Author of the conference Benoist, Yves.
Bibliography
- Broise-Alamichel, A., Parkkonen, J., & Paulin, F. (2016). Equidistribution and counting under equilibrium states in negatively curved spaces and graphs of groups. Applications to non-Archimedean Diophantine approximation.
