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Abstract: In 2006, Yeend introduced the notion of a topological higher-rank graph, generalising both Katsura's topological graphs and Kumjian and Pask's $k$-graphs. Yeend associated to each topological higher-rank graph $\Lambda$ a groupoid $\mathcal{G}_\Lambda$ and hence a $C^*$-algebra $C^*(\Lambda)$. However, except under additional hypotheses, the obstructions to proving versions of the standard uniqueness theorems for $C^*(\Lambda)$ using groupoid technology have proven substantial.\par In this talk we discuss how product systems of Hilbert bimodules and the notion of co-universal properties can be used to realise Yeend's algebras and establish the missing uniqueness theorems.
This talk will be accessible to graduate students.
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