Geometry and Topology Seminar

In this talk, we will briefly review the history of tight contact structures on small Seifert fibered spaces. We will introduce a new classification strategy for tight contact structures on Seifert fibered spaces. As an example, we will classify tight structures on every surgery of every torus knot in the 3-spehre. As a consequence, we will disprove the conjecture of Ghiggini and Van Horn-Morris about symplectic fillings on a family of Brieskorn spheres.