Résumé : The study of maps (graphs embedded into surfaces) is a rich subject at the crossroads of mathematics, computer science and theoretical physics. In this talk I will review the slice decomposition of planar maps : it started as a reformulation of some (by now) classical bijections between planar maps and trees, but then evolved into a general framework applicable to many families of maps and to their scaling limits. For simplicity I will restrict to the easiest setting of bipartite maps with controlled face degrees. I will explain how slice decomposition allows to enumerate pointed rooted maps, then "cylinders" and "pairs of pants" (planar maps with two and three boundaries, respectively). The talk is based on joint works with Emmanuel Guitter and Grégory Miermont.
[Slides.pdf] [arXiv] [vidéo]
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