Speaker: Boris Adamczewski (Claude Bernard University Lyon 1)
17 February, 2021 14:30 UTC
Abstract: It is commonly expected that expansions of numbers in multiplicatively independent bases, such as 2 and 10, should have no common structure. However, it seems extraordinarily difficult to confirm this naive heuristic principle in some way or another. In the late 1960s, Furstenberg suggested a series 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 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 the language of automata theory to formulate some related conjectures that formalize and express in a different way the same general heuristic. I will explain how the latter follow from some recent advances in Mahler’s method; a method in transcendental number theory initiated by Mahler in the end of the 1920s. This a joint work with Colin Faverjon.