BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Álvaro Bustos-Gajardo (The Open University) DTSTART:20221025T120000Z DTEND:20221025T130000Z DTSTAMP:20260423T021318Z UID:OWNS/97 DESCRIPTION:Title: Qu asi-recognizability and continuous eigenvalues of torsion-free S-adic syst ems\nby Álvaro Bustos-Gajardo (The Open University) as part of One Wo rld Numeration seminar\n\n\nAbstract\nWe discuss combinatorial and dynamic al descriptions of S-adic systems generated by sequences of constant-lengt h morphisms between alphabets of bounded size. For this purpose\, we intro duce the notion of quasi-recognisability\, a strictly weaker version of re cognisability but which is indeed enough to reconstruct several classical arguments of the theory of constant-length substitutions in this more gene ral context. Furthermore\, we identify a large family of directive sequenc es\, which we call "torsion-free"\, for which quasi-recognisability is obt ained naturally\, and can be improved to actual recognisability with relat ive ease.\n\nUsing these notions we give S-adic analogues of the notions o f column number and height for substitutions\, including dynamical and com binatorial interpretations of each\, and give a general characterisation o f the maximal equicontinuous factor of the identified family of S-adic shi fts\, showing as a consequence that in this context all continuous eigenva lues must be rational. As well\, we employ the tools developed for a first approach to the measurable case.\n\nThis is a joint work with Neil Mañib o and Reem Yassawi.\n LOCATION:https://researchseminars.org/talk/OWNS/97/ END:VEVENT END:VCALENDAR