We give an introduction to partially wrapped Fukaya categories of surfaces with orbifold singularities. Dissecting an orbifold surface $\mathbf S$ into polygons, certain dissections give rise to formal generators, inducing a triangulated equivalence between the derived Fukaya category of $\mathbf S$ and the perfect derived category of a graded associative algebra. This provides a geometric means for obtaining associative algebras -- conjecturally all -- which are derived equivalent to skew-gentle algebras. We include a new perspective on the partially wrapped Fukaya category of an orbifold disk which serves as a local model for the Fukaya categories of general orbifold surfaces. This perspective yields an equivalence between the perfect derived category of a quiver of type $\mathrm D_{ n+1}$ and the perfect derived category of a graded quiver of type $\widetilde{ \mathrm A}_{ n-1}$, the latter being equipped with quadratic zero relations and a nontrivial A$_\infty$ structure. This equivalence elucidates the relationship between skew-gentle algebras and orbifold surfaces, and the role of deformation theory in this relationship.
Categories: math.RT math.RA math.SG