Sira Gratz "Metric completions of discrete cluster categories"

Methods for generating new triangulated categories from old are notoriously few and far between. Neeman’s recent innovation  allows one to complete with

This promises the opportunity to construct a plethora of new examples of triangulated categories. However, up to now, explicit computations have all taken place within an existing ambient triangulated category. In this talk, based on joint work with Charley Cummings, we present a cluster-flavoured example where the computation can be done without this crutch. More specifically, we investigate discrete cluster categories of type A and show that, with a suitable choice of metric, the metric completion of such a category mirrors a topological completion of its combinatorial model.