Colloquium: Tuesday March 21, 2023. Speaker: Christopher Phillips (Oregon). Title: “Relations between dynamics and C*-algebras: Mean dimension and radius of comparison”.
room 614, Science & Education building.
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Speaker : Christopher Phillips (Oregon)
Date : Tuesday, 21st of March, 2023.
Time : 14:00
Title: Relations between dynamics and C*-algebras: Mean dimension and
radius of comparison.
Abstract: For an action of an amenable group on a compact metric space~, the mean dimension
was introduced by Lindenstrauss and Weiss.
It is designed so that the mean dimension of the shift on
is~. Its motivation was unrelated to C*-algebras.
The radius of comparison of a C*-algebra~
was introduced by Toms to distinguish counterexamples
in the Elliott classification program.
The algebras he used have nothing to do with dynamics.
A construction called the crossed product associates
a C*-algebra to a dynamical system .
Despite the apparent lack of connection between these concepts,
there is significant evidence for the conjecture that
when the action is free and minimal.
We will explain the concepts above; no previous knowledge
of mean dimension, C*-algebras, or radius of comparison will be assumed.
Then we describe some of the evidence.
In particular, we give the first general partial results
towards the direction
We don’t get the exact conjectured bound,
but we get nontrivial results for many of the known examples
of free minimal systems with