We show that the dimer algebra of a connected Postnikov diagram in the disc is bimodule
internally-Calabi–Yau in the sense of the author's earlier work [43]. As a consequence, we …

By work of a number of authors, beginning with Scott and culminating with Galashin and
Lam, the coordinate rings of positroid varieties in the Grassmannian carry cluster algebra …

We show that the coordinate ring of an open positroid variety coincides with the cluster
algebra associated to a Postnikov diagram. This confirms conjectures of Postnikov, Muller …

Abstract Let\, Gr\,^ ∘ (k, n) ⊂\, Gr\,(k, n) Gr∘(k, n)⊂ Gr (k, n) denote the open positroid
stratum in the Grassmannian. We define an action of the extended affine d-strand braid …

We introduce some new Frobenius subcategories of the module category of a preprojective
algebra of Dynkin type, and we show that they have a cluster structure in the sense of Buan …

We describe a categorification of the cluster algebra structure of multihomogeneous
coordinate rings of partial flag varieties of arbitrary Dynkin type using Cohen–Macaulay …

We associate a dimer algebra to a Postnikov diagram (in a disc) corresponding to a cluster
of minors in the cluster structure of the Grassmannian. We show that is isomorphic to the …

These are notes taken by the second author for a series of three lectures by the first author
on absolute and relative Calabi-Yau completions and Calabi-Yau structures given at the …

Let $ Q $ be a finite quiver without oriented cycles, and let $\Lambda $ be the corresponding
preprojective algebra. Let $\mathfrak {g} $ be the Kac-Moody Lie algebra with Cartan datum …

This is an introduction to some aspects of Fomin-Zelevinsky's cluster algebras and their links
with the representation theory of quivers and with Calabi-Yau triangulated categories. It is …