The talk is based on my ongoing project concerning the derived Picard groups of graded gentle algebras, or equivalently, partially wrapped Fukaya categories of surfaces in the sense of Haiden-Katzarkov-Kontsevich. After recalling some previous results in the ungraded case, I will explain the structure of these groups and the main ingredients of this result. As such, we discuss a projection map from the derived Picard group to the mapping class group and mapping class group actions on these categories. The last ingredient is the use of exponential maps to determine the kernel of the projection map. I will explain how they allow us to integrate certain Hochschild classes of any A-Infinity-algebra over a field of characteristic 0, to elements in its derived Picard group.