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{\Large Department of Mathematics, BGU}

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{\Huge BGU Probability and Ergodic Theory  (PET) seminar}\\[0.2\baselineskip]

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\textbf{On} \emph{Thursday, June 11, 2026}
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\textbf{At} \emph{11:10 -- 12:00}
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\textbf{In} \emph{-101}

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{\large\scshape Ilan Hirshberg}
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will talk about
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{\Large\bfseries Long and thin covers and crossed product C*-algebras\par}
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\textsc{Abstract:}
Nuclear dimension, introduced by Winter and Zacharias, is an invariant for C\emph{-algebras which generalizes covering dimension for compact Hausdorff spaces, and plays an important role in structure theory for amenable C}-algebras. It is usually mainly interesting to show that it is finite, as opposed to computing its actual value. Given an action of a group G on a locally compact Hausdorff space X, one forms the crossed product C*-algebra C\_0(X) \textbackslash{}rtimes G; this construction has been heavily studied in the field.

I will discuss joint work with Jianchao Wu, in which we find bounds on the nuclear dimension of nuclear dimension of the crossed product for a large class of group actions, including arbitrary actions of finitely generated virtually nilpotent groups on finite dimensional spaces and certain boundary actions of hyperbolic groups. This involves introducing a notion of “long and thin covers” which serves as the appropriate generalization of Rokhlin-type towers for non-free actions.  As another application of the result, we generalize a result of Joseph and construct a family of profinite actions of wreath products of finite abelian groups by Z\^{}d which are allosteric (that is, are minimal and topologically free, but not essentially free, meaning that fixed points sets are meager but have non-zero measure with respect to the unique invariant measure), and show that the resulting crossed product are well behaved from the perspective of structure and classification of C*-algebras.

As the paper is rather long, in the talk I will just give an overview of some of the definitions and techniques, intended for people from dynamical systems who are not experts in C*-algebras.








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