Ilan Hirshberg, Ben Gurion University of the Negev
"Mean dimension and radius of comparison"
The concept of mean dimension for topological dynamics was developed by Lindenstrauss and Weiss, based on ideas of Gromov. Independently, and for different reasons entirely, Toms introduced the concept of radius of comparison for C*-algebras. It appears, however, that there is a connection between those two notions: to each topological dynamical system one can associate a C*-algebra (known as the crossed product or the transformation group C*-algebra), and there appears to be a connection between the mean dimension of the dynamical system and the radius of comparison of the associated C*-algebra.
I will try to explain those concepts, their origin, a new related concept which we call mean cohomological independence dimension (in joint work in preparation with N. Christopher Phillips), and what is known about the connection between them.
The talk will not assume familiarity with C*-algebras or topological dynamics.
MC 5501