Venue   British Mathematical Colloquium 2013, University of Sheffield, 28 March 2013. Abstract   (Joint work with Simon Willerton) Magnitude is a real-valued invariant of metric spaces, springing from a category-theoretic 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 real-valued function on the positive real line. Roughly, the Convex Magnitude Conjecture states that for convex subsets of Rn, 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.   This page was last changed on 13 April 2013. You can go to an extremely short introduction to Beamer, or home.