Georgia Institute of Technology College of Sciences

Contact geometry in three dimensions is a land of two disjoint classes ofcontact structures; overtwisted vs. tight. The former ones are flexible,means their geometry is determined by algebraic topology of underlying twoplane fields. In particular their existence and classification areunderstood completely. Tight contact structure, on the other hand, arerigid. The existence problem of a tight contact structure on a fixed threemanifold is hard and still widely open. The classification problem is evenharder. In this talk, we will focus on the classification of tight contactstructures on Seifert fibered manifolds on which the existence problem oftight contact structures was settled recently by Lisca and Stipsicz.