Abstract

In this talk we describe an ongoing project to construct the adjoint (symplectic) groupoids associated to elliptic Poisson structures. These are a type of Poisson structure that is nondegenerate outside of a submanifold of codimension two. We will describe the geometry of these structures and see that their behavior depends on their so-called elliptic residue, and consequently so do the groupoids. Tools that are used in our constructions are the blow-up procedure for groupoids of Gualtieri-Li, a normal form result due to Witte, and the fact that elliptic Poisson manifolds can be blown-up to be log-Poisson, as noticed by Cavalcanti-Gualtieri.