William Da Silva: Integrability of critical Fortuin-Kasteleyn planar maps

mardi 31 mars 2026, 10:30 → 11:30 Europe/Paris

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 q<4 and collapse when q>4. 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. Berestycki..