The magnitude of graphs and finite metric spaces


Venue   Workshop on Topology and Neuroscience, EPFL, Lausanne, 30 November 2018

Summary   Magnitude is a numerical invariant defined in wide categorical generality, and therefore applicable to many kinds of mathematical object. In topology and algebra, magnitude is closely related to Euler characteristic. For subsets of Euclidean space, it combines classical geometric invariants such as volume, surface area and perimeter. But I will focus here on the cases of graphs and finite metric spaces. Here, it is less clear what magnitude "means", but it appears to convey useful information about dimensionality and number of clusters. There is even a magnitude homology theory available (due to Hepworth, Willerton and Shulman), lifting magnitude from a numerical to an algebraic invariant. I will give an overview.

Slides   In this pdf file. See this bibliography for references and further reading.

This page was last changed on 3 December 2018. You can read an extremely short introduction to Beamer, or go home.