Ana Balibanu (Harvard), The wonderful compactification and the universal centralizer

Let G be a complex semisimple algebraic group of adjoint type and bar{G} the wonderful compactification. We show that the closure in G of the centralizer G^e of a regular nilpotent e in Lie(G) is isomorphic to the Peterson variety. We generalize this result to show that for any regular x in Lie(G), the closure of the centralizer G^x in G is isomorphic to the closure of a general G^x -orbit in the flag variety. We consider the family of all such centralizer closures, which is a partial compactification of the universal centralizer. We show that it has a natural log-symplectic Poisson structure that extends the usual symplectic structure on the universal centralizer.