Ana Balibanu (Mar. 4, 2022): Regular centralizers and the wonderful compactification

The universal centralizer of a complex semisimple adjoint group G is the family of regular centralizers in G, parametrized by the regular conjugacy classes. It has a natural symplectic structure which is inherited from the cotangent bundle of G. I will construct a smooth, log-symplectic relative compactification of this family using the wonderful compactification of G. Its compactified centralizer fibers are isomorphic to Hessenberg varieties, and its symplectic leaves are indexed by root system combinatorics. I will also explain how to produce a multiplicative analogue of this construction, by moving from the Poisson to the quasi-Poisson setting.