Algebras from surfaces: deformation, duality, quotients

There are a number of constructions which start with a (suitably decorated) surface together with a triangulation or more general system of arcs and produce an algebra, possibly differential-graded or A-infinity. Examples include: gentle algebras, Jacobian and Ginzburg algebras of surfaces, Brauer graph algebras, as well as generalizations of these. I will review some of these constructions and discuss recently discovered connections between them, involving deformation, Koszul duality, and cyclic group quotients. Based on joint work with Merlin Christ and Yu Qiu (arXiv:2303.18249).