**Ricardo Mendes,
University of Oklahoma**

**Title:**
A geometric take on Kostant's Convexity Theorem

**Abstract:** We characterize convex subsets of R^{n}
invariant under the linear action of a compact group G, by identifying
their images in the orbit space R^{n}/G by a purely metric
property. As a consequence, we obtain a version of Kostant's
celebrated Convexity Theorem (1973) whenever the orbit space
R^{n}/G is isometric to another orbit space
R^{m}/H. (In the classical case G acts by the adjoint
representation on its Lie algebra R^{n}, and H is the Weyl
group acting on a Cartan sub-algebra R^{m}). Being purely
metric, our results also hold when the group actions are replaced with
submetries.