BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Izabella Łaba (University of British Columbia) DTSTART:20221005T160000Z DTEND:20221005T170000Z DTSTAMP:20260423T021149Z UID:HAeS/36 DESCRIPTION:Title: Fa vard length estimates via cyclotomic divisibility\nby Izabella Łaba ( University of British Columbia) as part of Harmonic analysis e-seminars\n\ n\nAbstract\nThe Favard length of a planar set $E$ is the average length o f its one-dimensional projections. It is well known (due to Besicovitch) t hat if $E$ is a purely unrectifiable planar self-similar set of Hausdorff dimension 1\, then its Favard length is 0. Consequently\, if $E_\\delta$ i s the $\\delta$-neighbourhood of $E$\, then the Favard length of $E_\\delt a$ goes to 0 as $\\delta\\to 0$. A question of interest in geometric measu re theory\, ergodic theory and analytic function theory is to estimate the rate of decay\, both from above and below. Partial results in this direct ion have been proved by many authors\, including Mattila\, Nazarov\, Perez \, Volberg\, Bond\, Bateman\, and myself. In addition to geometric measure theory\, this work has involved methods from harmonic analysis\, additive combinatorics\, and algebraic number theory. I will review the relevant b ackground\, and then discuss my recent work with Caleb Marshall on upper b ounds on the Favard length for 1-dimensional planar Cantor sets with a rat ional product structure. This improves on my earlier work with Bond and Vo lberg\, and incorporates new methods introduced in my work with Itay Londn er on integer tilings.\n LOCATION:https://researchseminars.org/talk/HAeS/36/ END:VEVENT END:VCALENDAR