Séminaires : Séminaire d'Algèbre

This is a report on recent work in collaboration with Norihiro Hanihara (arXiv:2512.03836). We develop a differential graded enhancement of Amiot's construction of Calabi-Yau structures on Verdier quotients. Using this framework, we establish the existence of a right Calabi-Yau structure on the dg singularity category associated with a symmetric order. Combining this with a structure theorem in collaboration with Bernhard Keller, we establish a triangle equivalence between the singularity category with a cluster-tilting object and the cluster category associated with a Calabi-Yau dg algebra. We also construct a left Calabi-Yau structure on the bounded dg derived category of a symmetric order, which is a non-commutative analogue of a result by Brav-Dyckerhoff.

This talk will take place on Zoom only.