Georgia Institute of Technology College of Sciences

One of the fundamental problems in contact topology is to classify contact structures on a given 3-manifold. In particular, classifying contact structures on surgeries along a given knot has been very poorly studied. The only fully understood case so far is that of the unknot 
(lens spaces); for all other knots we have only partial results, or none at all. Several topological and algebraic tools have been developed to 
attack this problem. In this talk, we discuss recent developments and the strategy for classifying tight contact structures on surgeries along torus knots. This is joint work with John Etnyre, Bülent Tosun, and Konstantinos Varvarezos.