Abstract:
We are going to discuss two colorful Carathéodory theorems for strongly convex hulls, generalizing the colorful Caratéodory theorem for ordinary convexity by Imre Bárány, the non-colorful Carathéodory theorem for strongly convex hulls by the speaker, and the “very colorful theorems’’ by Andreas Holmsen and others.
We will try to understand if the assumption of a "generating convex set” is really needed in such results; and will discuss a topological criterion for one convex body to be a Minkowski summand of another.
