Wednesday, November 2, 14:00, 8.122
Dong Yang, The interplay between 2- and 3- CYs.

Abstract:
I will give a survey talk on the recent progress on the interplay between 2-CYs and 3-CYs. The theory was motivated by the categorification of cluster algebras using on the one hand 2-CY categories by Buan--Marsh--Reineke--Reiten--Todorov, Caldero--Chapoton, Caldero--Keller,... and on the other hand 3-CY categories by Kontsevich--Soibelman. I will briefly discuss the constructions of 3-CY categories by Ginzburg and by Kontsevich--Soibelman. Then I will move on to Amiot's construction of 2-CY categories from 3-CY ones. The construction in the opposite direction has also been studied by many people, e.g. Amiot--Iyama--Reiten--Todorov, de Voelscey--Van den Bergh. Of particular interest is de Voelscey--Van den Bergh's approach. I will close with an example from 3-dimensional McKay correspondence.