Category Theory 2010, Genova, 23 June 2010.
Abstract In mathematics, many objects come with a canonical notion of size: sets have cardinality, vector spaces have dimension, topological spaces have Euler characteristic, and so on. A categorical approach illuminates the connections between these invariants and throws up at least two more, the Euler characteristic of a category and the magnitude of a metric space.
In ecology, on the other hand, there are some long-standing questions about biodiversity. How should one quantify it? And, if we are given a list of species from which to build a community, in what proportions should the species be represented in order to maximize the community's diversity?
As we shall see, the answer to the maximum diversity question is surprisingly categorical — in both senses of the word.
References Tom Leinster, A maximum entropy theorem with applications to the measurement of biodiversity, arXiv:0910.0906 (2009).
Tom Leinster, Christina Cobbold, Measuring diversity: the importance of species similarity. Ecology, in press (doi:10.1890/2402-1).
Slides In this pdf file.