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Dalhousie-AARMS AAMP Seminar: Reem Yassawi (Open University, London)

November 6, 2020 @ 4:00 pm - 5:00 pm

Title: Some tame or wild Cantor dynamical systems

Abstract: A topological dynamical system is a pair (X,T) where X is a compact metric spaces and T is a group or semigroup acting continuously on X. One algebraic invariant of a such a dynamical system is the Ellis semigroup.  The Ellis semigroup E(X,T) of a topological dynamical system is defined to be the compactification of the action T in the topology of pointwise convergence on the space of all function X^X.  Tameness is a concept whose roots date back to Rosenthal’s \ell^1 embedding theorem, which says that if a sequence in \ell^1 does not have a weakly Cauchy subsequence, then it must be a sequence on unit vectors in \ell^1.  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 \beta \mathbb{N}, the Stone-Cech compactification of \mathbb{N}.

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.

Details

Date:
November 6, 2020
Time:
4:00 pm - 5:00 pm
Event Category:
Website:
https://sureshes.wordpress.com/dalhousie-analysis-seminar/

Venue

Zoom seminar

Organizer

Suresh Eswarathasan
Email:
sr766936@dal.ca

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