Invitation to (random) planar maps
Abstract
The field of planar maps is relatively young. They were introduced in the 1960s through the work of William T. Tutte. Since then, they have been intensely studied in many directions: in enumerative and bijective combinatorics, topology, probability, algebra, statistical physics, and quantum physics. This talk will be an opportunity to introduce the notion of planar maps and to explore their combinatorial properties. We will also see how they serve as a relevant prototype for defining random geometric spaces. Finally, we will briefly illustrate, through the Ising model, how these random geometries provide an interesting framework for statistical physics.