Abstract: The Poincare Conjecture states that S^3 is the only closed, simply-connected, three-dimensional manifold. Since any 3-manifold can be constructed by Dehn surgery on a knot or link, one way to attack this conjecture is by looking at finite surgeries, i.e., surgeries which result in a manifold with finite fundamental group.
Boyer and Zhang have shown that a hyperbolic knot admits at most five finite surgeries. In this talk I will report on recent work showing that a large class of pretzel knots admit at most one non-trivial finite surgery.