Georgia Institute of Technology College of Sciences

It is an important and rather difficult problem in low dimensional topology to determine which rational homology 3-spheres bound smooth rational homology 4-balls. This is largely open even in the case of Brieskorn spheres—a special class of Seifert fibered spaces. In this talk, we will focus on symplectic version of this question, and (almost) determine when a small Seifert fibered space admits a symplectic rational homology ball filling. For some small Seifert fibered spaces, we provide explicit and new examples of such fillings, and for most others we provide strong restrictions. In the talk, we will review these concepts and provide further context; give some details of the techniques involved and finally mention a few applications. This will report on recent joint work with J. Etnyre and B. Özbağcı.