On the classification of tight contact structures on Lens spaces

The goal of this talk is to state the classification of tight contact structures on Lens spaces, and in particular, highlight some of the modern techniques used to get this classification result such as convex surface decomposition and bypasses. Using these techniques, the classification becomes a problem about a certain set of curves on tori and the mapping class group of such tori. The result then brings together a simple but interesting connection between the mapping class group of the torus, the Farey tessellation and continued fractions via the group SL(2,Z).