Exploring random maps: slicing, peeling and layering - 2

The combinatorial theory of maps, or graphs on surfaces, is rich of many different approaches (recursive decompositions, algebraic approches, matrix integrals, bijective approaches) which often have probabilistic counterparts that are of interest when one wants to study geometric aspects of random maps. In these lectures, I will review parts of this theory by focusing on three different decompositions of maps, namely, the slice decomposition, the peeling process, and the decomposition in layers, and by showing how these decompositions can be used to give access to quite different geometric properties of random maps.