QLunch: Faces and orbits in invariant convex sets and cones
Speaker: Howard Barnum, University of Copenhagen and University of New Mexico
Title: Faces and orbits in invariant convex sets and cones
Convex compact sets invariant under a group of affine transformations, and convex cones invariant under a group of linear transformations, are mathematically interesting and have a wide range of applications in physics, optimization, statistical modeling, and beyond. I'll present some of what is known about how the face structure of such convex sets is related to the structure of the group representation in which they are embedded, from both the existing literature and my ongoing work in this area. The consequences of transitive action of the automorphism group of a cone on its interior ("homogeneity") and transitive action of the automorphism group of a convex compact set on its extreme boundary ("reversible transitivity") will especially be explored.
Howard N. Barnum
Guest Professor, Department of Mathematical Sciences,
University of Copenhagen (March--December 2017)