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SUMMARY:Boris Adamczewski (Institut Camille Jordan & CNRS)
DTSTART:20210329T111500Z
DTEND:20210329T121500Z
DTSTAMP:20260423T023056Z
UID:WarsawNT/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WarsawNT/26/
 ">Furstenberg's conjecture\, Mahler's method\, and finite automata</a>\nby
  Boris Adamczewski (Institut Camille Jordan & CNRS) as part of Warsaw Numb
 er Theory Seminar\n\nLecture held in currently online.\n\nAbstract\nIt is 
 commonly expected that expansions of numbers in multiplicatively independe
 nt bases\, such as 2 and 10\, should have no common structure. However\, i
 t seems extraordinarily difficult to confirm this naive heuristic principl
 e in some way or another. In the late 1960s\, Furstenberg suggested a seri
 es of conjectures\, which became famous and aim to capture this heuristic.
  The work I will discuss in this talk is motivated by one of these conject
 ures. Despite recent remarkable progress by Shmerkin and Wu\, it remains t
 otally out of reach of the current methods. While Furstenberg’s conjectu
 res take place in a dynamical setting\, I will use instead the language of
  automata theory to formulate some related problems that formalize and exp
 ress in a different way the same general heuristic. I will explain how the
  latter can be solved thanks to some recent advances in Mahler’s method\
 ; a method in transcendental number theory initiated by Mahler at the end 
 of the 1920s. This a joint work with Colin Faverjon.\n
LOCATION:https://researchseminars.org/talk/WarsawNT/26/
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