The University of Michigan Combinatorics Seminar
An orbitope is the convex hull of an orbit of a compact group G acting linearly on a vector space. Orbitopes are the simplest convex bodies which possess many symmetries. Some, particularly those in low-dimensional representations of G, have very beautiful structure. Our interest is in whether or not these appealing convex bodies are spectahedra, that is, if they are described by a system of linear matrix inequalities, preferably with coefficients in the field of definition of the orbitope.
In this talk, I will introduce orbitopes and discuss spectahedra and the new field of convex algebraic geometry in which these questions lie. I will illustrate this with orbitopes for SO(2) and for the special orthogonal group acting on trace-free symmetric matrices.
This is joint work with Raman Sanyal and Bernd Sturmfels.