English
Counting and equidistribution of integral representations by quadratic norm forms in positive characteristic?
Multi angle
Auteurs : Paulin, Frédéric (Auteur de la Conférence)
CIRM (Editeur )
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 (Editeur )
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Résumé :
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.
Codes MSC : 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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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 15/02/17 Date de captation : 09/02/17 Sous collection : Research School arXiv category : Dynamical Systems ; Number Theory Domaine : Dynamical Systems & ODE ; Number Theory Format : MP4 (.mp4) - HD Durée : 01:03:47 Audience : Researchers ; Graduate Students Download : https://videos.cirm-math.fr/2017-02-09_Paulin.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Homogeneous spaces, diophantine approximation and stationary measures / Espaces homogenes. Approximation diophantienne. Mesures stationnairesOrganisateurs de la rencontre : Adamczewski, Boris ; Athreya, Jayadev ; Mercat, Paul ; Palesi, Frédéric Dates : 06/02/17 - 10/02/17 Année de la rencontre : 2017 URL Congrès : http://conferences.cirm-math.fr/1712.html
Données de citation
DOI : 10.24350/CIRM.V.19119103Citer cette vidéo: 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 |
Voir aussi
- [Multi angle] Shrinking targets on homogeneous spaces and improving Dirichlet's Theorem / Auteur de la Conférence Kleinbock, Dmitry.
- [Multi angle] Dynamics on quotients of SL(2,C) by discrete subgroups - Lecture 2 / Auteur de la Conférence Schapira, Barbara.
- [Multi angle] Dynamics on homogeneous spaces and Diophantine approximation / Auteur de la Conférence Ghosh, Anish.
- [ Post-edited] Dense subgroups in simple groups - Lecture 2 / Auteur de la Conférence Benoist, Yves.
Bibliographie
- 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.
