Colorful theorems for strong convexity (joint with Andreas Holmsen)

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.