Deformations of graded gentle algebras and Fukaya categories of surfaces
By Barmeier Severin
A thread quiver consists of a quiver together with a collection of linearly ordered posets that replace some (or all) arrows. From a thread quiver, we construct a 𝑘-linear category C where objects are the vertices of the quiver and the elements of the associated posets; and bases of morphism spaces are given by ‘paths’. We study the category of pointwise finite dimensional representations of C (possibly quotients of C by weakly admissible ideals). An important example arises when we simply consider the real line equipped with its natural order. In this case, representations correspond to 1-parameter persistence modules, which play a key role in topological data analysis. One of our main goals is to study the indecomposable objects and decompositions of pointwise finite dimensional representations. We then analyse the bounded derived category and how to use it to construct new cluster categories, when the threadings satisfy some additional conditions. Interestingly, cluster categories from thread quivers include situations in which a Serre functor does not exist. This talk is based on two joint projects with C. Paquette