Workshop on Flows, Foliations and Contact Structures

An interesting aspect of the classification of symplectic fillings of Seifert fibered spaces is the appearance of complex and symplectic line arrangements in CP2. Line arrangements have been studied classically for decades and have intricate combinatorial and geometric realization properties, but little is known about their topological and symplectic realizations. In joint work with Danny Ruberman, we find obstructions to topological realizations of certain configurations. I will discuss how various types of information about symplectic realizations of line arrangements can be used to produce interesting symplectic fillings of Seifert fibered spaces and contact graph manifolds which are tight but not sympletically fillable.