
Venue
British Mathematical
Colloquium 2013,
University of Sheffield,
28 March 2013.
Abstract (Joint work with Simon Willerton) Magnitude is a realvalued invariant of metric spaces, springing from a categorytheoretic study of size. Unlike most invariants of metric spaces, it changes unpredictably as the space is scaled up or down. It therefore assigns to each space a realvalued function on the positive real line. Roughly, the Convex Magnitude Conjecture states that for convex subsets of R^{n}, this function is a polynomial encoding all the most important quantities associated with convex sets: dimension, volume, surface area, perimeter, and so on. I will explain where magnitude comes from, how it is defined, and what makes the conjecture interesting. I will also explain the conjecture's unusual status: while there is compelling evidence in its favour, not a single nontrivial example is known. Slides In this pdf file. The final page contains clickable links to references.
