On Cosmetic Surgeries on Knots

The cosmetic surgery conjecture says that no pair of Dehn surgeries on a knot along inequivalent slopes yield orientation preservingly homeomorphic 3-manifolds. After introducing several known results, I will talk about some recent results concerning certain two-bridge knots. Also I will present a new example of a hyperbolic knot admitting a pair of of Dehn surgeries yielding orientation reversingly homeomorphic hyperbolic 3-manifolds. This talk is based on joint works with Toshio Saito and In Dae Jong.