Coadjoint orbitopes via symplectic and complex geometry

An orbitope is the convex hull of an orbit of a compact Lie group acting linearly on a vector space. In this talk we will discuss the convex hull of a coadjoint orbit (i.e. a coadjoint orbitope) and we will describe how  the face structure of this convex body can be studied by means of the momentum map.  We will also explain the link between Satake-Furstenberg compactifications and coadjoint orbitopes, which is one of  the motivations to study these convex bodies.