Speaker: 范俐，中国科学院晨兴数学中心

Inviter: 方明

Title: On relative Koszul duality and cluster categories

Language: Chinese

Time & Venue: 2026.09.04 10:30-11:30 南楼N820

Abstract: We study three related realizations of cluster categories: via orbit categories, singularity categories and cosingularity categories. Motivated by the construction of cluster categories as (co)singularity categories, we show that, for any dg algebra A, its perfect derived category can be realized in two ways: firstly, as an (enlarged) cluster category of a certain differential bigraded algebra, generalizing a result of Ikeda–Qiu, and secondly, as a (shrunk) singularity category of another differential bigraded algebra, generalizing a result of Happel following Hanihara. We relate these two descriptions using a version of relative Koszul duality. We also explain how dg orbit categories and dg quotients fit into this picture, with an application to collapsing gradings for higher cluster categories arising from bigraded Calabi–Yau completions as introduced by Ikeda–Qiu. This is joint work with Bernhard Keller and Yu Qiu.