The ubiquitous interrelations between algebraic geometry and physics has for centuries flourished fruitful phenomena in both fields. With connections made as far back as Archimedes whose work on conic sections aided development of concepts surrounding the motion under gravity, physical understanding has largely relied upon the mathematical tools available. In the modern era, these two fields are still heavily intertwined, with particular relevance in addressing one of the most significant problems of our time - quantising gravity. String theory as a candidate for this theory of everything, relies heavily on algebraic geometry constructions to define its spacetime and to interpret its matter. However, where new mathematical tools arise their implementation is not always simple.

Having learnt of the remarkable theorem of Bely ˇ ı [1] which relates the existence of algebraic models of Riemann surfaces to that of analytic properties of rational functions thereon, Grothendieck launched an entire programme [2] by pictorially representing 1 this structure as bipartite graphs (the dessin) drawn on the Riemann surface. He hypothesised dessins d'enfants in their current form as a conceptual representation of the absolute Galois group over the rationals, one the most mysterious and least understood objects in number theory. Subsequently, he developed a generalisation of Bely ˇ ı's theorem which extends the surfaces considered in the mapping to more general Riemann surfaces. Properties of the mapping are identified with combinatorial invariants of the dessin d'enfant graphs [2] (q.v.