BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Carlo Pagano DTSTART:20230531T140000Z DTEND:20230531T150000Z DTSTAMP:20260422T102921Z UID:FGC-IPM/36 DESCRIPTION:Title: Abelian arboreal representations\nby Carlo Pagano as part of FGC-HRI- IPM Number Theory Webinars\n\n\nAbstract\nI will present joint work with A ndrea Ferraguti which makes progress on a Conjecture of Andrews and Petsch e that classifies abelian dynamical Galois groups over number fields\, in the unicritical case. I will explain how to reduce the conjecture to the p ost-critically finite case and the key tools to handle all unicritical PCF with periodic critical orbit over any number field and all PCF over quadr atic number fields. Along the way I will present an earlier rigidity resul t of ours on the maximal closed subgroup of the automorphism group of a bi nary rooted tree\, which offered us with the main input to translate the c ommutativity of the Galois image into diophantine equations. I will also o verview progress on the tightly related problem of lower bounding arboreal degrees.\n\nZoom Meeting ID: 856 1386 0958 Passcode: 513992\n LOCATION:https://researchseminars.org/talk/FGC-IPM/36/ END:VEVENT END:VCALENDAR