The mathematics of diversity


Venue   University of Ottawa colloquium and 2021 Category Theory Novemberfest, 12 November 2021

Abstract   What is the mathematical definition of diversity? Ecologists have debated how best to measure diversity for over 70 years, and the same question arises in multiple fields both in the life sciences and beyond. But it is only just now being appreciated that diversity is also a fertile source of new mathematics. It is closely related to entropy (already a core concept in subjects such as information theory), and indeed, sheds new light on this old concept. The story I will tell begins with category theory, passes through parts of geometry and analysis, and ends with an answer to the question: what is the canonical probability measure on a metric space?

Slides   In this pdf file.

of diversity and magnitude concepts

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