Geometric models of Ginzburg algebras via local-to-global principles

The derived categories of different classes of algebras (e.g. gentle algebras) and dg-algebras (e.g. Ginzburg algebras of triangulated surfaces) have recently been described in terms of surfaces, in so-called geometric models. Results include the description of objects in terms of curves in a surface and Hom’s in terms of intersections. These algebras have in common that they arise via gluing, i.e. as the global sections of a constructible cosheaf. In the talk, we will describe the gluing construction for (relative) Ginzburg algebras of triangulated surfaces and compare it with the gluing construction for gentle algebras. We will then discuss how the gluing constructions naturally lead to the geometric models of their derived categories.