Dehn filling is a fundamental tool in group theory, appearing in the solution of the Virtual Haken Conjecture, the study of the Farrell-Jones and Baum-Connes Conjecture, the isomorphism problem of relatively hyperbolic groups, and the construction of purely pseudo-Anosov normal subgroups of mapping class groups. In this talk, I will discuss past joint work with Bin Sun on the cohomology of Dehn filling quotients and our recent results on their L^2-Betti numbers. The applications include the verification of the Singer Conjecture for certain Einstein manifolds, virtual fibering, and the construction of new examples of hyperbolic groups with exotic subgroups.
