String domains for coadjoint orbits

Partial tropicalizations are a kind of Poisson manifold built using techniques of Poisson-Lie theory and the geometric crystals of Berenstein-Kazhdan. They provide a bridge between linear Poisson manifolds and cones which parametrize the canonical bases of irreducible $G$-modules. 

 

I will talk about applications of partial tropicalization theory to questions in symplectic geometry. For each regular coadjoint orbit of a compact group, we construct an exhaustion by symplectic embeddings of toric domains. As a by-product we arrive at a conjectured formula for the Gromov width of coadjoint orbits. We prove similar results for multiplicity-free spaces. This is joint work with A. Alekseev, J. Lane, and Y. Li.