Merlin Christ (University of Hamburg), Graded Brauer graph algebras and constructible sheaves of categories, I and II.

Abstract:

Constructible sheaves on graphs are of a combinatorial nature: they assign a value to each vertex and to each edge of the graph, and a morphism to each incidence of a vertex and an edge. We will survey how one can construct and study classed of derived categories of associative (dg-)algebras using such constructible sheaves on graphs, with values in enhanced triangulated categories (stable infinity-categories). The main examples will be graded Brauer graph algebras. Their Koszul dual dg-algebras are given by quotients of Ginzburg dg-algebras associated with triangulated surfaces. As an application of the sheaf description, one can obtain a (partial) geometric model, relating their representation theory with the geometry of a marked surface. Partially based on joint work with F. Haiden and Y. Qiu.