Vortrag im Schwerpunkt Reelle Geometrie und Algebra
Freitag, 24. Juli 2009, um 14:15 Uhr in F426 (Schwerpunktkolloquium) Raman Sanyal (Berkeley)
Orbitopes
An orbitope is the convex hull of an orbit in a representation of a compact group G.
For finite groups this construction yields some of the nicest polytopes, among them the
regular polytopes and permutahedra. For general compact groups, orbitopes are
usually non-polytopal convex bodies. In this talk, I report on some recent results regarding
the spectrahedral representation and facial structure of some orbitopes for the groups O(d)
and SO(d). In some sense, these convex bodies can be viewed as continuous analogs of certain
well-known polytopes. This is joint work with Frank Sottile and Bernd Sturmfels.
