Colloquium: Tuesday, January 21, 2020. Speaker: Sefi Ladkani (Haifa). Title: “Stratifications of posets, derived equivalences and Calabi-Yau properties”.
Place: Room 614 in the Education & Sciences Building
Being fractionally Calabi-Yau is a periodicity property of triangulated categories introduced by Kontsevich more than 20 years ago. It is quite rare that a finite-dimensional algebra has derived category of modules which is fractionally Calabi-Yau, nevertheless it is conjectured that for many posets (partially ordered sets) arising in algebraic combinatorics, their incidence algebras do have this property.
Viewing posets as finite topological spaces, one can speak on their stratifications. I will explain how certain stratifications give rise to derived equivalences between the incidence algebra of a given poset and other algebras which are quotients of incidence algebras.
We use this result to establish the fractionally Calabi-Yau property for a large family of posets of partitions. In addition, we achieve significant progress towards proving a conjecture of Chapoton concerning the equivalences of the derived categories of posets of Dyck paths and the Tamari lattices.
Joint work with F. Chapoton and B. Rognerud.
Tea will be served before the talk (at 13:50).