BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Demi Allen (University of Exeter) DTSTART:20251209T150000Z DTEND:20251209T160000Z DTSTAMP:20260423T022037Z UID:NEDNT/98 DESCRIPTION:Title: R ectangular Shrinking Targets on Self-Similar Carpets\nby Demi Allen (U niversity of Exeter) as part of New England Dynamics and Number Theory Sem inar\n\nLecture held in Online.\n\nAbstract\nSuppose $(X\,d)$ is a metric space equipped with a Borel probability measure\, and suppose $(B_i)_{i \\ in \n}$ is a sequence of measurable sets in $X$. Suppose $T: X \\to X$ is a measure preserving transformation\, and consider the set \n$\\{x \\in X: T^n x \\in B_n \\text{ for infinitely many } n\\in\n\\}$. \nThis is a shr inking target set. The terminology of "shrinking targets" was first introd uced by Hill and Velani in 1995. Since then\, shrinking target problems ha ve received a great deal of interest\, especially with regards to studying the measure-theoretic and dimension-theoretic properties of shrinking tar get sets. In this talk\, I will discuss some recent work with Thomas Jorda n (Bristol\, UK) and Ben Ward (York\, UK) where we establish the Hausdorff dimension of a shrinking target set where our "targets" (the $B_n$) are r ectangles and $X$ is a self-similar carpet.\n LOCATION:https://researchseminars.org/talk/NEDNT/98/ END:VEVENT END:VCALENDAR