Hyperbolic Dehn Surgery

Hyperbolic Dehn Surgery is a procedure for producing closed hyperbolic 3-manifolds from hyperbolic knot complements, by 'filling in the cusp' with a solid torus. This procedure produces infinitely many examples of closed hyperbolic manifolds, as Thurston (its discoverer) proved that all but finitely many ways of performing the gluing result in a manifold which admits a hyperbolic structure. This talk provides a graduate-student-friendly introduction to this area of mathematics, leading up to the statement (but not proof) of Thurston's theorem, and placing it in the wider context of geometric topology and geometric group theory.