Recent developments in the minimal model program in positive characteristic and birational geometry have found purchase within Arithmetic Geometry, e.g., around questions of exceptional sets involved in Manin's conjecture on points of bounded height. In turn, arithmetic perspectives afforded by Manin's conjecture are starting to shed light on the geometry of spaces of rational curves. Our goal in this workshop is to bring together two camps of geometers (birational and arithmetic) who have had few opportunities to interact on a large scale. The points of contact so far are amenable to explicit computations, e.g., determination of presentations of Cox rings for Fano varieties, finite field method applications to stable rationality problems, algorithms to compute Peyre's constant in Manin's conjecture, point counts on spaces of rational curves, and these computational problems will form an important component of the workshop, which will be complemented with theoretical developments.