$n$-cluster tilting subcategories of module categories are the prototypical setting of Iyama's higher dimensional Auslander-Reiten theory. Much attention has been given to algebras of global dimension n, for which there is at most one $n$-cluster tilting subcategory. For higher global dimension the notion of $n$-cluster tilting has certain drawbacks, which motivates the stronger notion of $n\mathbb Z$-cluster tilting due to Iyama and Jasso. It has been shown by Kvamme that an $n\mathbb Z$-cluster tilting subcategory of the module category gives rise to an $n\mathbb Z$-cluster tilting subcategory of the singularity category.

In my talk I will present a classification of $n\mathbb Z$-cluster tilting subcategories for Nakayama algebras. Moreover, I will show which $n\mathbb Z$-cluster tilting subcategories they give rise to in the corresponding singularity categories.

This talk is based on joint work with Sondre Kvamme and Laertis Vaso.