Title: Quantum graphs, convex bodies, and a century-year-old problem of Minkowski
Abstract: That the ball minimizes surface area among all sets of fixed volume, was known since antiquity; this is equivalent to the fact that the ball is unique set which yields equality in the isoperimetric inequality. But the isoperimetric inequality is only a very special case of quadratic inequalities about mixed volumes of convex bodies, whose equality cases were unknown since the time of Minkowski. This talk is about these quadratic inequalities and their unusual equality cases which we resolved using spectral theory. No prior knowledge of the subject is assumed. Joint work with Ramon van Handel.