Deformations of graded gentle algebras and Fukaya categories of surfaces
Deformation theory of associative algebras is controlled by Hochschild cohomology and usually involves an intricate obstruction calculus. In the case of gentle algebras, the deformation theory turns out to admit a nice explicit description. I will explain how (graded or ungraded) gentle algebras can be deformed as 𝐴∞-algebras or associative algebras. All such deformations admit a natural description in terms of the geometric surface model for their derived categories, which also illuminates the relationship between gentle and skew-gentle algebras.