English
Contracting self-similar groups and conformal dimension
Multi angle
Auteurs : Nekrashevych, Volodymyr (Auteur de la Conférence)
CIRM (Editeur )
CIRM (Editeur )
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Résumé :
One can associate with every finitely generated contracting self-similar group (for example, with the iterated monodromy group of a sub-hyperbolic rational function) and every positive $p$ the associated $\ell_{p}$-contraction coefficient. The critical exponent of the group is the infimum of the set of values of $p$ for which the $\ell_{p}$-contraction coefficient is less than 1. Another number associated with a contracting self-similar group is the Ahlfors-regular conformal dimension of its limit space. One can show that the critical exponent is not greater than the conformal dimension. However, the inequality may be strict. For example, the critical exponent is less than 1 for many groups of intermediate growth (while the corresponding conformal dimension is equal to 1 ). We will also discuss a related notion of the degree of complexity of an action of a group on a set.
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 02/11/2021 Date de captation : 20/09/2021 Sous collection : Research talks arXiv category : Group Theory ; Dynamical Systems Domaine : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Durée : 00:59:08 Audience : Researchers Download : https://videos.cirm-math.fr/2021-09-20_Nekrashevych.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexeOrganisateurs de la rencontre : Benini, Anna Miriam ; Drach, Kostiantyn ; Dudko, Dzmitry ; Hlushchanka, Mikhail ; Schleicher, Dierk Dates : 20/09/2021 - 24/09/2021 Année de la rencontre : 2021 URL Congrès : https://conferences.cirm-math.fr/2546.html
Données de citation
DOI : 10.24350/CIRM.V.19813903Citer cette vidéo: Nekrashevych, Volodymyr (2021). Contracting self-similar groups and conformal dimension . CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19813903 URI : http://dx.doi.org/10.24350/CIRM.V.19813903 |
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