Calabi-Yau structures on Drinfeld quotients and Amiot's conjecture

In 2009, Claire Amiot gave a construction of Calabi-Yau structures on Verdier quotients. We sketch how to lift it to the dg setting. We use this construction as an important step in an outline of the proof of her conjecture on the structure of 2-Calabi-Yau triangulated categories with a cluster-tilting object.