Title: Topological and fractal properties of non-integer base expansions
Abstract: In 1957 A. Rényi generalized the usual integer base expansions to non-integer bases. This led to interesting and deep problems in number theory, combinatorics, set theory, probability, measure and ergodic theory, symbolic dynamics and topology. Here we mostly discuss the uniqueness of expansions.
The talk is based on joint research with P. Erdős, I. Joó, P. Loreti, A. Pethő, M. Pedicini, M. de Vries, A.C. Lai, M. Baatz, S. Akiyama, D. Kong and W. Li.