Séminaires à venir

In this talk, we introduce numeration systems in rational bases (as defined by Akiyama, Frougny and Sakarovitch) and extend this definition to quadratic algebraic bases by giving an algorithm to expand complex numbers. We show how these numeration systems induce a tiling of the plane, and characterize expansions in terms of -adic completions, following Steiner and Thuswaldner. These numeration systems belong to a larger class of dynamical systems called shift radix systems: we give an overview, present some current lines of research and pose some open questions. The talk features several examples and images and no prior knowledge on numeration systems is required.