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{\Large Department of Mathematics, BGU}

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{\Huge Operator Algebras and Operator Theory}\\[0.2\baselineskip]

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\textbf{On} \emph{Monday, December 12, 2022}
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\textbf{At} \emph{16:00 -- 17:00}
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\textbf{In} \emph{-101 (basement)}

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{\large\scshape Adam Dor-On 
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  (University of Haifa)
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will talk about
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{\Large\bfseries Co-universality for Toeplitz algebras of random walks on relatively hyperbolic groups\par}
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\textsc{Abstract:}
When studying quotients of C\emph{-algebras generated by creation and annihilation operators on analogues of Fock space, the question of the existence of a co-universal quotient plays an important role in answering fundamental questions in the theory. The study of co-universal quotients goes back to works of Cuntz, and Cuntz and Krieger, on uniqueness theorems for C}-algebras arising from symbolic dynamics, and by now co-universal quotients have been shown to exist in several broad classes of examples of Toeplitz C*-algebras.

When associating Toeplitz C\emph{-algebras to random walks on a group \$G\$, new notions of *ratio-limit space} and \emph{boundary} emerge from searching for their co-universal quotients, and the existence of these co-universal quotients becomes intimately related to the group dynamics on the ratio-limit boundary.

In this talk I will exlain how we extended results of Woess to show that there is co-universal quotient for a large class of symmetric random walks on relatively hyperbolic groups. This sheds light on some questions of Woess on ratio-limits for random walks on relatively hyperbolic groups, and extends a result mine on the existence of co-universal quotients for Toeplitz C*-algebras for random walks.

*This talk is based on joint work with Ilya Gekhtman.








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