An S-adic characterization of linear-growth complexity subshifts

Bastián Espinoza
Universidad Andrés Bello, Santiago, Chili

Date(s) : 12/09/2023   iCal
15 h 00 min - 16 h 00 min

In the context of symbolic dynamics, the class of “linear-growth complexity subshifts” is of particular relevance as it occurs in a variety of areas, such as geometric dynamical systems, language theory, number theory, and numeration systems, among others. During the intensive study carried out on this subject since the beginning of the 90s, it was proposed that a hierarchical decomposition based on -adic sequences that characterizes linear-growth complexity subshifts would be useful to understand this class. The problem of finding such a characterization was given the name “-adic conjecture” and inspired several influential results in symbolic dynamics. In this talk, I will present an -adic characterization of this class as well as some of its applications, giving in particular a solution to this conjecture.


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