In these two talks, we will start by introducing a result which establishes the existence and uniqueness of (DG) enhancements for triangulated categories which admit an additive generator whose endomorphism algebra is finite-dimensional (over a perfect field). We will then present a generalisation of this result that allows us to treat a larger class of triangulated categories, which instead admit a generator with a strong regularity property (a so-called dZ-cluster tilting object). We will also explain how our result, combined with crucial theorems of August and Hua-Keller, leads to a positive solution of the Donovan-Wemyss Conjecture for contraction algebras as observed by Keller. We will also comment on some details about the proof.
