Naszódi Márton: John ellipsoids of revolution

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 Sagmeister, we study the problem of finding the largest volume ellipsoid of revolution in K.