Rokhlin dimension is a numerical invariant for actions of various classes of groups on C*-algebras. It is a generalization of the Rokhlin property, which is Rokhlin dimension zero. The main interest in this concept has been that finite Rokhlin dimension serves as a regularity property: one can prove that various properties of C*-algebras are preserved under forming crossed products, provided the action has finite Rokhin dimension. However, no attention was paid to the actual value of the dimension, and indeed for actions on simple C*-algebras, it was not known whether there are actions with values other than 0,1 or 2. We recently constructed examples of finite group actions on simple AF algebras with arbitrarily large values of Rokhlin dimension, thereby showing that this is an interesting invariant, which could be thought of as a measure of the complexity of the group action. I'll explain the concepts above and outline the idea of the proof.

This is joint work with N. Christopher Phillips.

Bio: Ilan Hirshberg is an Israeli mathematician, who works in operator algebras. He earned his doctorate from UC Berkeley in 2003 under the supervision of Bill Arveson. He works as a professor at Ben-Gurion University.