Information, Geometry, and Physics Seminar

Magnitude is a numerical isometric invariant of metric spaces defined recently by Tom Leinster, based on considerations from category theory. Despite the subject's youth, it has found connections with other invariants from a large and growing number of fields, including theoretical ecology, graph theory, topological data analysis, potential theory, and integral geometry. I will discuss the basic definitions and motivation and give a broad survey of these connections, ending with some applications in high-dimensional convexity.