Multiple zeta values in geometry and number theory

Abstract

Multiple zeta values are a mysterious class of real numbers that appear in many branches of pure mathematics and in theoretical physics. I will explain some of the basic theory and problems surrounding multiple zeta values (from a more algebraic or number theoretic viewpoint). I will then discuss where multiple zeta values (or slight generalisations thereof) appear some more geometric or analytic contexts, such as the area expansion of families of constant mean curvature surfaces (as studied by Heller, Heller and Traizet), or in the Dirichlet eigenvalues of regular polygons (as studied by Berghaus, Georgiev, Monien and Radchenko).