BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Monika Kudlinska (Oxford) DTSTART:20230523T130000Z DTEND:20230523T150000Z DTSTAMP:20260423T023017Z UID:WienGAGT/37 DESCRIPTION:Title: Profinite rigidity and free-by-cyclic groups\nby Monika Kudlinska (O xford) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbst ract\nIt is a natural question to ask how much algebraic information is en coded in the set of finite quotient of a given group. More precisely\, one tries to establish which properties of infinite\, discrete\, residually f inite groups are preserved under isomorphisms of their profinite completio ns. A group is said to be (absolutely) profinitely rigid if its isomorphis m type is completely determined by its profinite completion. The first tal k will focus on the history of this problem\, covering some classical resu lts as well as more recent work and open problems in the area. We will int roduce all the necessary background\, so no prior knowledge of the topic w ill be assumed.\n\nA variation of this problem involves restricting to a c ertain family of groups and trying to decide whether a group is profinitel y rigid relative to this family. Much work has been done towards solving t his problem for fundamental groups of 3-manifolds. In the second talk\, we will focus our attention on a related family of groups known as free-by-c yclic groups\, which have natural connections with 3-manifolds. We will se e that many properties of free-by-cyclic groups are invariants of their pr ofinite completion. As a consequence\, we obtain various profinite rigidit y results\, including the almost profinite rigidity of generic free-by-cyc lic groups amongst the class of all free-by-cyclic groups. \n\nThis is joi nt work with Sam Hughes.\n LOCATION:https://researchseminars.org/talk/WienGAGT/37/ END:VEVENT END:VCALENDAR