Cosmetic surgeries and Chern-Simons invariants

Dehn surgery is an important construction in low-dimensional topology that describes all three-manifolds. The Cosmetic Surgery Conjecture predicts two different Dehn surgeries on the same knot always gives different three-manifolds. We discuss how a certain object from gauge theory, the Chern-Simons functional, can help approach this problem. This is joint work with Mike Miller Eismeier.