BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Henna Koivusalo (University of Vienna) DTSTART:20200602T123000Z DTEND:20200602T133000Z DTSTAMP:20260423T021354Z UID:OWNS/54 DESCRIPTION:Title: Li near repetition in polytopal cut and project sets\nby Henna Koivusalo (University of Vienna) as part of One World Numeration seminar\n\n\nAbstra ct\nCut and project sets are aperiodic point patterns obtained by projecti ng an irrational slice of the integer lattice to a subspace. One way of cl assifying aperiodic sets is to study repetition of finite patterns\, where sets with linear pattern repetition can be considered as the most ordered aperiodic sets. \nRepetitivity of a cut and project set depends on the sl ope and shape of the irrational slice. The cross-section of the slice is k nown as the window. In an earlier work it was shown that for cut and proje ct sets with a cube window\, linear repetitivity holds if and only if the following two conditions are satisfied: (i) the set has minimal complexity and (ii) the irrational slope satisfies a certain Diophantine condition. In a new joint work with Jamie Walton\, we give a generalisation of this r esult for other polytopal windows\, under mild geometric conditions. A key step in the proof is a decomposition of the cut and project scheme\, whic h allows us to make sense of condition (ii) for general polytopal windows. \n LOCATION:https://researchseminars.org/talk/OWNS/54/ END:VEVENT END:VCALENDAR