BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Emmanuel Rauzy (Université de Paris) DTSTART:20220201T160000Z DTEND:20220201T170000Z DTSTAMP:20260423T022744Z UID:CTA/75 DESCRIPTION:Title: Com putable analysis on the space of marked groups\nby Emmanuel Rauzy (Uni versité de Paris) as part of Computability theory and applications\n\n\nA bstract\nI will present some results that concern the study of Markovian c omputable analysis on the topological space of marked groups. While this w ork was originally motivated by questions in group theory\, it turned out to be also very interesting from the point of view of computable analysis alone\, providing the first naturally arising Polish space that is not eff ectively Polish.\nIndeed\, while it is effectively complete and separable\ , the space of marked groups is not effectively separable: any sequence th at is dense in it is non-computable. I will also present a phenomenon of f ailure of an effective axiom of choice: there is no algorithm that can\, g iven a non-empty basic clopen set\, produce a group that belongs to this s et. Because of this\, none of the well known results of Kreisel-Lacombe-Sc hoenfield\, Ceitin and Moschovakis\, and that establish the effective cont inuity of computable functions in different settings\, can be applied to t he space of marked groups.\nMy talk will focus on presenting some classica l theorems of the theory of decision problems for groups (Boone-Novikov\, Boone-Rogers\, etc)\, in order to show how those theorems apply to the spa ce of marked groups.\n LOCATION:https://researchseminars.org/talk/CTA/75/ END:VEVENT END:VCALENDAR