BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lucía Rossi (Montanuniversität Leoben) DTSTART:20211116T133000Z DTEND:20211116T143000Z DTSTAMP:20260423T052836Z UID:OWNS/65 DESCRIPTION:Title: Ra tional self-affine tiles associated to (nonstandard) digit systems\nby Lucía Rossi (Montanuniversität Leoben) as part of One World Numeration seminar\n\n\nAbstract\nIn this talk we will introduce the notion of ration al self-affine tiles\, which are fractal-like sets that arise as the solut ion of a set equation associated to a digit system that consists of a base \, given by an expanding rational matrix\, and a digit set\, given by vect ors. They can be interpreted as the set of “fractional parts” of this digit system\, and the challenge of this theory is that these sets do not live in a Euclidean space\, but on more general spaces defined in terms of Laurent series. Steiner and Thuswaldner defined rational self-affine tile s for the case where the base is a rational matrix with irreducible charac teristic polynomial. We present some tiling results that generalize the on es obtained by Lagarias and Wang: we consider arbitrary expanding rational matrices as bases\, and simultaneously allow the digit sets to be nonstan dard (meaning they are not a complete set of residues modulo the base). We also state some topological properties of rational self-affine tiles and give a criterion to guarantee positive measure in terms of the digit set.\ n LOCATION:https://researchseminars.org/talk/OWNS/65/ END:VEVENT END:VCALENDAR