August 21, 2018

Simon Willerton (Sheffield),

*The magnitude of odd balls*

**Abstract:**Tom Leinster introduced the magnitude of finite metric spaces by formal analogy with his notion of Euler characteristic of finite categories. This can be thought of an 'effective number of points' of the metric space. This simple idea has turned out to have connections with all sorts of mathematics, including diversity measurement, Hausdorff dimension, categorification, semi-classical analysis and curvature measures. In this talk I'll give a fair amount of background and then focus on obtaining a formula for the magnitude of odd dimensional balls, explaining what it has to do with nineteenth century integrals and twentieth century enumerative combinatorics.