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Abstract

Classifying complex objects by simpler invariants is a common goal in many branches of pure mathematics as well as science more generally. One famous example is the classification of elements by their atomic number. But as remarkable as such a classification is, by itself it doesn't tell us, for example, what colour a particular element is — to answer that question, we need a physical realisation of the element, and then it becomes easy to see what colour it is. There is a similar interplay between classification and realisations (or "constructions") of objects in pure mathematics, and in my talk I will discuss examples of this interplay, with a view to outlining new constructions of a certain class of classifiable C*-algebras based on group actions on trees.

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