The place of diversity in pure mathematics


Venue   Boyd Orr Conference 2014, Boyd Orr Centre for Population and Ecosystem Health, University of Glasgow, 18 July 2014.

Summary   Diversity is a ubiquitous feature of biological systems, from the scale of the molecule to the rainforest. Being able to quantify it accurately is crucial in dozens of disparate biological contexts.

But it is not only in biological contexts that the concept of diversity is important. I will show how fundamentally, diversity is a mathematical concept. Moreover, I will argue that it is not something at the fringes of mathematics, but is closely related to core mathematical quantities that have been studied continuously since the time of Euclid. The concept of diversity has even become useful for proving theorems in entirely pure mathematics, and I will finish by mentioning an example of such a theorem due to Mark Meckes (arXiv:1308.5407, Corollary 7.4).

Slides   In this pdf file.

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