Algebraic and Combinatorial Invariants of Subshifts and Tilings
This conference will gather researchers working on different topics such as combinatorics, computer science, probability, geometry, physics, quasicrystallography, ... but sharing a common interest: dynamical systems and more precisely subshifts, tilings and group actions. It will focus on algebraic and dynamical invariants such as group automorphisms, growth of symbolic complexity, Rauzy graphs, dimension groups, cohomology groups, full groups, dynamical spectrum, amenability, proximal pairs, ... With this conference we aim to spread out these invariants outside of their original domains and to deepen their connections with combinatorial and dynamical properties.
7
2021
7
5 Stunden 25 Minuten
7 Ergebnisse
54:35
Matte Bon, NicolásA subgroup of a group is confined if the closure of its conjugacy class in the Chabauty space does not contain the trivial subgroup. Such subgroups arise naturally as stabilisers for non-free actions on compact spaces. I will explain a result establishing a relation between the confined subgroup of a group with its highly transitive actions. We will see how this result allows to understand the highly transitive actions of a class of groups of dynamical origin. This is joint work with Adrien Le Boudec.
2021Centre International de Rencontres Mathématiques (CIRM)
1:02:38
Donoso, SebastiánI will comment on recent results concerning the topological properties of finite rank Cantor minimal systems. I will mention some ideas to estimate their word complexity and ask a few open problems.
2021Centre International de Rencontres Mathématiques (CIRM)
06:10
2Durand, Fabien et al.This conference will gather researchers working on different topics such as combinatorics, computer science, probability, geometry, physics, quasicrystallography, ... but sharing a common interest: dynamical systems and more precisely subshifts, tilings and group actions. It will focus on algebraic and dynamical invariants such as group automorphisms, growth of symbolic complexity, Rauzy graphs, dimension groups, cohomology groups, full groups, dynamical spectrum, amenability, proximal pairs, ... With this conference we aim to spread out these invariants outside of their original domains and to deepen their connections with combinatorial and dynamical properties.
2021Centre International de Rencontres Mathématiques (CIRM)
1:02:37
1Lukina, OlgaWe consider infinite interval exchange transformations (IETs) obtained as a composition of a finite IET and the von Neumann-Kakutani map, called rotated odometers, and study their dynamical and ergodic properties by means of an associated Bratteli-Vershik system. We show that every rotated odometer is measurably isomorphic to the first return map of a rational parallel flow on a translation surface of finite area with infinite genus and a finite number of ends, with respect to the Lebesgue measure. This is one motivation for the study of rotated odometers. We also prove a few results about the factors of the unique minimal subsystem of a rotated odometer. This is joint work with Henk Bruin.
2021Centre International de Rencontres Mathématiques (CIRM)
53:22
2Salo, VilleWe say a pointed dynamical system is asymptotically nilpotent if every point tends to zero. We study group actions whose endomorphism actions are nilrigid, meaning that for all asymptotically nilpotent endomorphisms the convergence to zero is uniform. We show that this happens for a large class of expansive group actions on a large class of groups. The main examples are cellular automata on subshifts of finite type.
2021Centre International de Rencontres Mathématiques (CIRM)
1:00:06
1Fickenscher, JonSubshifts on finite alphabets form a class of dynamical systems that bridge topological/ergodic dynamical systems with that of word combinatorics. In 1984, M. Boshernitzan used word combinatorics to provide a bound on the number of ergodic measures for a minimal subshift with bounds on its linear factor complexity growth rate. He further asked if the correct bound for subshifts naturally coded by interval exchange transformations (IETs) could be obtained by word combinatoric methods. (The ”correct” bound is roughly half that obtained by Boshernitzan’s work.) In 2017 and joint with M. Damron, we slightly improved Boshernitzan’s bound by restricting to a smaller class of subshifts that still contained IET subshifts. In recent work, we have further proved the ”correct” bound to subshifts whose languages satisfy a specific word combinatoric condition, which we called the Regular Bispecial Condition. (This condition is equivalent to being Eventually Dendric as independently introduced by F. Dolce and D. Perrin.) During the same time we worked on our 2017 paper, V. Cyr and B. Kra were independently improving Boshernitzan’s results. In 2019, they relaxed the conditions to no longer require minimality and extended Boshernitzan’s bound to generic measures. (Generic measures are those that have generic points, meaning they satisfy the averaging limits as stated in Pointwise Ergodic Theorem. However, there are non-ergodic generic measures.) We have obtained the improved 2017 bound but for generic measures (and on a more general class of subshifts). It should be noted that, to our current knowledge, there does not exist a proof of the correct bound of generic measures for minimal IETs (by any method).In this talk, I will discuss these recent results and highlight related open problems.
2021Centre International de Rencontres Mathématiques (CIRM)
25:49
1Durand, FabienInterview de Fabien Durand, mathématicien à l'Université de Picardie Jules Verne, président de la Société Mathématique de France depuis le 1er juillet 2020.
2021Centre International de Rencontres Mathématiques (CIRM)