BEGIN:VCALENDAR VERSION:2.0 PRODID:-//wp-events-plugin.com//7.2.3.1//EN TZID:Europe/Paris X-WR-TIMEZONE:Europe/Paris BEGIN:VEVENT UID:5472@i2m.univ-amu.fr DTSTART;TZID=Europe/Paris:20241029T110000 DTEND;TZID=Europe/Paris:20241030T160000 DTSTAMP:20241028T134543Z URL:https://www.i2m.univ-amu.fr/evenements/workshop-on-random-substitution s/ SUMMARY:Eden Delight\, Pierre Arnoux\, Dan Rust\, Andrew Mitchell\, Tony Sa muel (...): Workshop on Random Substitutions DESCRIPTION:Eden Delight\, Pierre Arnoux\, Dan Rust\, Andrew Mitchell\, Ton y Samuel: Workshop on Random Substitutions\nOrganised by :\nEden Delight P . Miro\n(Ateneo de Manila University)\nAnd\nPierre Arnoux\n(Université d' Aix-Marseille)\nTuesday\, October 29\n11:00 - Eden Delight P. Miro: Random substitutions and\ntheir associated dynamical systems\n14:00 - Dan Rust: Periodicity and automorphism\ngroups for random substitutions\n15:00 - And rew Mitchell: Complexity and topological\nentropy of random substitution s hifts\nWednesday\, October 30\n10:00 - Tony Samuel: Complexity and geometr y of\naperiodic systems\n11:00 - Pierre Arnoux: Higher dimensional extensi ons of\nsubstitutions\n14:00 - Open problems\, research questions : Discus sion\n\nAbstracts\n\nEden Delight Miro\nDepartment of Mathematics\, Ateneo de Manila University\, Katipunan Avenue\, 1108\, Quezon City\, Philippine s\nTitle: Random substitutions and their associated dynamical systems\nAbs tract: One way to construct interesting symbolic dynamical systems is via substitution rules\nover a finite alphabet\, whereby each letter of the al phabet is assigned a predetermined word. A\nnatural generalization of this is to consider maps called random substitutions that assign to each\nlett er a finite set of possible images with a probability distribution. In thi s talk\, I will discuss some\nbasic dynamical and topological properties o f the subshifts arising from random substitutions.\n\nDan Rust\nSchool of Mathematics and Statistics\, The Open University\, Milton Keynes\, MK7 6AA \, UK\nTitle: Periodicity and automorphism groups for random substitutions \nAbstract: Perhaps the most basic question for a symbolic dynamical syste m is whether it\nincludes periodic points or not. Amazingly\, a full class ification of random substitutions that admit\nperiodic points is still mis sing. In this talk\, I'll present some of the basic results in this direct ion\,\nincluding criteria for determining the existence or non-existence o f periodic points and\nalgorithms that apply to a large family of random s ubstitutions for finding periodic points if they\nexist\, and therefore al low us to enumerate them. I'll also discuss the symmetry groups for\nrando m substitutions\, which are very different from the automorphism groups fo r deterministic\nsubstitutions. For instance\, the automorphism groups for most random substitution subshfits\ncontain every finite group as a subgr oup. Nevertheless\, similar tools are used in their study\;\nnamely using the hierarchical structure of words.\n\nAndrew Mitchell\nSchool of Mathema tics and Statistics\, The Open University\, Milton Keynes\, MK7 6AA\, UK\n Title: Complexity and topological entropy of random substitution shifts\nA bstract: In contrast to their deterministic counterparts\, random substitu tion shifts often have\npositive topological entropy. In this talk\, I'll provide an overview of some recent developments in\nthe theory of topologi cal entropy for random substitution shifts. These include necessary and\ns ufficient conditions under which a primitive random substitution shift has positive entropy and a\nsystematic approach to calculating topological en tropy\, which can be leveraged whenever the\nrandom substitution has a wel l-defined inflation length. I'll also discuss how (non-primitive)\nrandom substitutions give rise to a broad variety of shifts with sub-exponential complexity\,\nincluding intermediate growth.\n\nTony Samuel\nMathematics a nd Statistics\, University of Exeter\, North Park Road\, Exeter\, UK\, EX4 4QF\nTitle: Complexity and geometry of aperiodic systems: Rauzy Fractals and Rauzy measures\nAbstract: Aperiodic sequences and sequence spaces form prototypical mathematical models of\nquasicrystals. The most quintessenti al examples include subshifts of Sturmian words and\nsubstitutions\, which are ubiquitous objects in ergodic theory and aperiodic order. Two of the\ nmost striking features these shift spaces have\, are that they have zero topological entropy and\nare uniquely ergodic. Random substitutions are a generalisation of deterministic substitutions\,\nand in stark contrast to their deterministic counterparts\, subshifts of random substitutions often \nhave positive topological entropy and exhibit uncountably many ergodic m easures.\nWe will begin by talking about subshifts generated by Sturmian w ords and ways to measure\ntheir complexity beyond topological entropy\, an d show how this measure of complexity can be\nused to build a classificati on via Jarník sets. We will then build a bridge between these subshifts\n and subshifts of random substitutions. We will conclude with some recent d ynamical results on\nsubshifts of random substitutions and ways to visuali se these subshifts. Namely\, we will present\na method to build a new clas s of Rauzy fractals and Rauzy measures.\n\nPierre Arnoux\nInstitut de Math ématiques de Marseille\, Université d'Aix-Marseille\, Campus de Luminy\, Case 907\, 13288 Marseille Cedex 9\nTitle: Higher dimensional extensions of substitutions and their dual maps\nAbstract: Words on a final alphabet of size d can be considered as coding broken lines in a\nspace of dimensio n d\, with vertices the abelianisation of all the prefixes of the word. Us ual\nsubstitutions can then be interpreted as acting on broken lines\, and in the case of Pisot\nsubstitutions\, this can be seen as an example of a model set. To extend the theory beyond the\nPisot case\, one would need t o extend to stepped surfaces\, or more generally to k-dimensional\nstepped manifolds.\nWe will show how this can be achieved\, giving a formalism fo r k-dimensional extensions\nof substitutions (or more generally\, free gro ups endomorphisms) and their dual maps. This\nallows us to study not only Pisot substitutions\, but more generally hyperbolic endomorphisms of\nfree groups. We will show some examples\, and a number of open questions. This formalism can\nbe combined with the S-adic framework and the idea of rand om substitutions.\n CATEGORIES:Workshop,Ernest LOCATION:I2M Luminy - TPR2\, Salle de Séminaire 304-306 (3ème étage)\, 1 63 Avenue de Luminy\, Marseille\, 13009\, France X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, Mars eille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=I2M Luminy - TPR2\, Sall e de Séminaire 304-306 (3ème étage):geo:0,0 END:VEVENT BEGIN:VTIMEZONE TZID:Europe/Paris X-LIC-LOCATION:Europe/Paris BEGIN:STANDARD DTSTART:20241027T020000 TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET END:STANDARD END:VTIMEZONE END:VCALENDAR