BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mathieu Sablik (Toulouse) DTSTART:20260127T140000Z DTEND:20260127T160000Z DTSTAMP:20260423T023011Z UID:WienGAGT/51 DESCRIPTION:Title: Self-simulable groups\nby Mathieu Sablik (Toulouse) as part of Vienn a Geometry and Analysis on Groups Seminar\n\n\nAbstract\nA configuration i s a colouring of a finitely generated group by a finite alphabet. A subshi ft of finite type is a set of configurations defined by a finite collectio n of forbidden patterns. Subshifts of finite type naturally arise in the s tudy of tilings and play are of great interest from a computational point of view and symbolic dynamics.\n\nIn the first part of the talk\, we will address several questions that are classical in the case Z^2\, but which l ead to new and largely unexplored phenomena for general finitely generated groups. These include:\n- existence of a subshift of finite type containi ng at most one element of the alphabet.\n- existence of a subshift of fini te type containing only aperiodic configurations (local rules force global behaviour).\n- decidability of the emptiness problem for subshift of fini te type\, given the set of forbidden patterns as input.\n\nIn the second p art of the talk\, we introduce a new class of groups. A finitely generated group is said to be self-simulable if every computable action of the grou p on an effectively closed zero-dimensional space is a topological factor of a subshift of finite type over that group. In other words\, any “reas onable” group action can be encoded by local rules. We will show that su ch groups do exist\, and that the class of self-simulable groups is stable under commensurability and under quasi-isometries among finitely presente d groups. Finally\, we will present several examples of self-simulable gro ups\, including Thompson’s group V and higher-dimensional general linear groups.\n\nThis is a joint work with Sebastian Barbieri and Ville Salo.\n LOCATION:https://researchseminars.org/talk/WienGAGT/51/ END:VEVENT END:VCALENDAR