BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jamie Walton (University of Nottingham) DTSTART:20260421T120000Z DTEND:20260421T130000Z DTSTAMP:20260423T034445Z UID:OWNS/166 DESCRIPTION:Title: G eometric recognisability for FLC patterns\nby Jamie Walton (University of Nottingham) as part of One World Numeration seminar\n\n\nAbstract\nInf ormally\, recognisability of a substitution (or ‘inflate\, subdivide’) rule regards its invertibility. Beyond the classical result of Mossé\, h ighly general recognisability results have recently been established in th e symbolic setting\, even going beyond substitutions to S-adic sequences. In this talk\, I will introduce a notion of a geometric tiling\, point set or generalised ‘pattern’ of Euclidean space being substitutional with respect to an inflation map\, in terms of two basic relations from Aperio dic Order: local derivability and local indistinguishability. These are an alogues\, from Symbolic Dynamics\, of being related by sliding block codes and being in the same orbit closure\, respectively. In the translational finite local complexity (FLC) case (e.g.\, tilings with finitely many tile types\, meeting in finitely many ways up to translation)\, we give a form ula for the number of pre-images of a pattern under substitution in terms of its group of translational periods. In particular\, for a suitable powe r of substitution\, the non-periodic tilings are precisely those with uniq ue pre-images under substitution. Many techniques used are similar to thos e in Solomyak’s unique composition result\, although we require no minim ality (primitivity) assumption. If time permits\, I will explain the motiv ation for this work\, on the question of when a cut and project scheme pro duces substitutional patterns.\n LOCATION:https://researchseminars.org/talk/OWNS/166/ END:VEVENT END:VCALENDAR