Q-Math Seminar
Separated graphs and dynamics
Speaker: Pere Ara (UAB)Date: Tuesday, 04 March 2025 - 13:00Place: Room 2.2.D08, Universidad Carlos III de Madrid
Online: https://eu.bbcollab.com/guest/22f7877a774148a3aee3e398a4a86380 (active on request)
Abstract:
A separated graph is a pair \((E,C)\), where \(E\) is a directed graph, \(C=\bigsqcup _{v\in E^ 0} C_v\), and \(C_v\) is a partition of \(r^{-1}(v)\) (into pairwise disjoint nonempty subsets) for every vertex \(v\). In recent years, separated graphs have been used to provide combinatorial models of several structures, often related to dynamical systems. This can be understood as a generalization of the common use of usual directed graphs in symbolic dynamics. I will survey some of these developments, including the failure of Tarski's dichotomy in the setting of topological actions, the construction of a family of ample groupoids with prescribed type semigroup, and the modeling of actions on the Cantor set.
