Numerous exciting results circle around the quality of specific power series: formal, convergent, algebraic, Gevrey, Mahler, D-finite, P-recursive, differentially algebraic, holonomic, hypergeometric, lacunary, G-functions, ..., with often sharp contrasts between characteristic zero and positive characteristic. 

For all these there are intriguing examples, counter-examples, particularities, results, techniques, comparisons, algorithms, computations, conjectures. We wish to get a more precise view on all this material in order to focus on particularly interesting problems and phenomena. The goal would be to design a prospective roadmap for future research and activities.

More info available here.