Fortuin-Kasteleyn (FK) maps are a classical model of discretized surfaces decorated with a percolation-like configuration, depending on a weight q > 0. Physicists predicted that the model undergoes a phase transition at q=4. Such a phase transition has been rigorously established by Scott Sheffield, who proved that the surfaces converge (in some suitable sense) to a non-degenerate limiting object when q4. In this talk, I will present a new integrable approach to this problem, which enables us to exactly solve the FK model on planar maps for q less than 4. In particular, this approach allows us to extract the convergence of the FK maps at the critical threshold q=4, which has remained opened since Sheffield’s work. The talk is based on joint works with X. Hu, E. Powell and M. D. Wong, and with N. <a href="http://Berestycki.

https://indico.math.cnrs.fr/event/15777/ » target= »_blank » title= »Berestycki.

https://indico.math.cnrs.fr/event/15777/ »>Berestycki.

https://indico.math.cnrs.fr/event/15777/