BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Olga Lukina (Leiden University) DTSTART:20230614T140000Z DTEND:20230614T150000Z DTSTAMP:20260422T102927Z UID:FGC-IPM/37 DESCRIPTION:Title: Weyl groups in Cantor dynamics\nby Olga Lukina (Leiden University) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nArboreal repres entations of absolute Galois groups of number fields are given by profinit e groups of automorphisms of regular rooted trees\, with the geometry of t he tree determined by a polynomial which defines such a representation. Th us arboreal representations give rise to dynamical systems on a Cantor set \, and allow to apply the methods of topological dynamics to study problem s in number theory. In this talk we consider the conjecture of Boston and Jones\, which states that the images of Frobenius elements under arboreal representations have a certain cycle structure. To study this conjecture\, we borrow from the Lie group theory the concepts of maximal tori and Weyl groups\, and introduce maximal tori and Weyl groups in the profinite sett ing. We then use this new technique to give a partial answer to the conjec ture by Boston and Jones in the case when an arboreal representations is d efined by a post-critically finite quadratic polynomial over a number fiel d. Based on a joint work with Maria Isabel Cortez.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/37/ END:VEVENT END:VCALENDAR