  We introduce a class of dg-algebras which generalize the classical Brauer
graph algebras. They are constructed from mixed-angulations of surfaces and
often admit a (relative) Calabi--Yau structure. We discovered these algebras
through two very distinct routes, one involving perverse schobers whose stalks
are cyclic quotients of the derived categories of relative Ginzburg algebras,
and another involving deformations of partially wrapped Fukaya categories of
surfaces. Applying the results of our previous work arXiv:2303.18249, we
describe the spaces of stability conditions on the derived categories of these
algebras in terms of spaces of quadratic differentials.
