Title: Some tame or wild Cantor dynamical systems

Abstract: A topological dynamical system is a pair where is a compact metric spaces and is a group or semigroup acting continuously on . One algebraic invariant of a such a dynamical system is the Ellis semigroup.  The Ellis semigroup of a topological dynamical system is defined to be the compactification of the action in the topology of pointwise convergence on the space of all function .  Tameness is a concept whose roots date back to Rosenthal’s embedding theorem, which says that if a sequence in does not have a weakly Cauchy subsequence, then it must be a sequence on unit vectors in .  Köhler linked the concept of tameness to the Ellis semigroup.  A system is tame if its Ellis semigroup has size at most the continuum.  Non-tame systems are very far from tame, as they must contain a copy of , the Stone-Cech compactification of .

In this talk, I will briefly survey the properties of the Ellis semigroup that make it an interesting object to study, and discuss recent developments concerning tameness.  I will then discuss Toeplitz shifts, which themselves have been studied extensively in this context and is the subject of some joint work with G. Fuhrmann and J. Kellendonk.

The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over Zoom.  If you would like to attend, please email the organizers for connection details.