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\title{$C^*$-algebras associated to topological $k$-graphs and Exel-Larsen systems}
\author{Paulette N. Willis}
\date{\today}

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\noindent (Joint work with Cynthia Farthing and Nura Patani)  Generalizing the construction of a topological graph from a singly generated dynamical system, Yeend describes a topological $k$-graph $\Lambda$ constructed from the data of a locally compact Hausdorff space $\Omega$ and family of local homeomorphisms that pairwise commute where the composition is defined.  When these maps are everywhere-defined, one may construct an Exel-Larsen system $(C_0(\Omega),\N^k,\alpha,L)$.  In this talk, I will describe these constructions and show that the product systems $X^\Lambda$, $X^{Lar}$ associated to the topological $k$-graph and Exel-Larsen system, respectively, are isomorphic.  It follows that the Cuntz-Pimsner algebras $\mathcal{O}_{X^\Lambda}$ and $\mathcal{O}_{X^{Lar}}$ are isomorphic.

This talk will not assume any prior knowledge of $C^*$-algebras, topological $k$-graphs, or Exel-Larsen systems.  Undergraduates and graduate students are encouraged to attend.
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