BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Boris Adamczewski (CNRS\, Université Claude Bernard Lyon 1) DTSTART:20210427T123000Z DTEND:20210427T133000Z DTSTAMP:20260423T021359Z UID:OWNS/42 DESCRIPTION:Title: Ex pansions of numbers in multiplicatively independent bases: Furstenberg's c onjecture and finite automata\nby Boris Adamczewski (CNRS\, Universit é Claude Bernard Lyon 1) as part of One World Numeration seminar\n\n\nAbs tract\nIt is commonly expected that expansions of numbers in multiplicativ ely independent bases\, such as 2 and 10\, should have no common structure . However\, it seems extraordinarily difficult to confirm this naive heuri stic principle in some way or another. In the late 1960s\, Furstenberg sug gested a series of conjectures\, which became famous and aim to capture th is heuristic. The work I will discuss in this talk is motivated by one of these conjectures. Despite recent remarkable progress by Shmerkin and Wu\, it remains totally out of reach of the current methods. While Furstenberg ’s conjectures take place in a dynamical setting\, I will use instead th e language of automata theory to formulate some related problems that form alize and express in a different way the same general heuristic. I will ex plain how the latter can be solved thanks to some recent advances in Mahle r’s method\; a method in transcendental number theory initiated by Mahle r at the end of the 1920s. This a joint work with Colin Faverjon.\n LOCATION:https://researchseminars.org/talk/OWNS/42/ END:VEVENT END:VCALENDAR