Topological dynamical systems, C*-algebras, K-theory - An introduction to the topics of the workshop

I will explain how the concept of topological groupoids provides a unifying framework for studying topological dynamics in a rather general sense, in particular with a view towards their associated C*-algebras and invariants like K-theory and homology.

An algebraist in Operator Algebras: a self-similar perspective

Examples are critical to the development of operator algebras. Algebraic structures and actions on geometries provide a rich source of examples. I will give an overview of some C*-algebras associated to self-similar actions.

Ample groupoids, topological full groups, algebraic K-theory spectra and infinite loop spaces

Topological groupoids describe orbit structures of dynamical systems by capturing their local symmetries. The group of global symmetries, which are pieced together from local ones, is called the topological full group. This construction gives rise to new examples of groups with very interesting properties, solving outstanding open problems in group theory. This talk is about a new connection between groupoids and topological full groups on the one hand and algebraic K-theory spectra and infinite loop spaces on the other hand. Several applications will be discussed. Parts of this connection already feature in work of Szymik and Wahl on the homology of Higman-Thompson groups.