Description
The largest volume ellipsoid $E$ contained in a convex body $K$ in d-dimensional space is a central object in convexity. Fritz John gave conditions in terms of the contact points of $K$ and $E$ guaranteeing that $E$ is of largest volume. In this ongoing joint work with Grigory Ivanov, Zsolt Lángi and Ádám Sagmeiszter, we study the problem of finding the largest volume ellipsoid of revolution in $K$.