BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jamie Walton (University of Glasgow) DTSTART:20211207T133000Z DTEND:20211207T143000Z DTSTAMP:20260423T021449Z UID:OWNS/67 DESCRIPTION:Title: Ex tending the theory of symbolic substitutions to compact alphabets\nby Jamie Walton (University of Glasgow) as part of One World Numeration semin ar\n\n\nAbstract\nIn this work\, joint with Neil Mañibo and Dan Rust\, we consider an extension of the theory of symbolic substitutions to infinite alphabets\, by requiring the alphabet to carry a compact\, Hausdorff topo logy for which the substitution is continuous. Such substitutions have bee n considered before\, in particular by Durand\, Ormes and Petite for zero- dimensional alphabets\, and Queffélec in the constant length case. We fin d a simple condition which ensures that an associated substitution operato r is quasi-compact\, which we conjecture to always be satisfied for primit ive substitutions on countable alphabets. In the primitive case this impli es the existence of a unique natural tile length function and\, for a reco gnisable substitution\, that the associated shift space is uniquely ergodi c. The main tools come from the theory of positive operators on Banach spa ces. Very few prerequisites will be assumed\, and the theory will be demon strated via examples.\n LOCATION:https://researchseminars.org/talk/OWNS/67/ END:VEVENT END:VCALENDAR