BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Christopher Porter (Drake University) DTSTART:20200929T200000Z DTEND:20200929T210000Z DTSTAMP:20260423T005722Z UID:CTA/24 DESCRIPTION:Title: Eff ective Dimension and the Intersection of Random Closed Sets\nby Christ opher Porter (Drake University) as part of Computability theory and applic ations\n\n\nAbstract\nThe connection between the effective dimension of se quences and membership in algorithmically random closed subsets of Cantor space was first identified by Diamondstone and Kjos-Hanssen. In this talk\ , I highlight joint work with Adam Case in which we extend Diamondstone an d Kjos-Hanssen's result by identifying a relationship between the effectiv e dimension of a sequence and what we refer to as the degree of intersecta bility of certain families of random closed sets (also drawing on work by Cenzer and Weber on the intersections of random closed sets). As we show\, (1) the number of relatively random closed sets that can have a non-empty intersection varies depending on the choice of underlying probability mea sure on the space of closed subsets of Cantor space---this number being th e degree of intersectability of a given family of random closed sets---and (2) the effective dimension of a sequence X is inversely proportional to the minimum degree of intersectability of a family of random closed sets\, at least one of which contains X as a member. Put more simply\, a sequenc e of lower dimension can only be in random closed sets with more branching \, which are thus more intersectable\, whereas higher dimension sequences can be in random closed sets with less branching\, which are thus less int ersectable\, and the relationship between these two quantities (that is\, effective dimension and degree of intersectability) can be given explicitl y.\n LOCATION:https://researchseminars.org/talk/CTA/24/ END:VEVENT END:VCALENDAR