Tom Leinster: "Entropy and diversity: the axiomatic approach"

Topos Institute Colloquium, 26th of October 2023. ——— Ecologists have been debating the best way to measure diversity for more than 70 years. The concept of diversity is relevant not only in ecology, but also in other fields such as genetics and economics, as well as being closely related to information entropy. The question of how best to quantify diversity has surprising mathematical depth. Indeed, a general study of invariants resembling cardinality and Euler characteristic led to the unifying notion of the magnitude of an enriched category - a quantity which is also closely related to the maximum diversity of a community of prescribed species. I will give a high-level overview of the concepts of entropy, diversity and magnitude, and how they fit together.