Abstract: This talk will be studying the critical regime of the planar random-cluster model on 
with cluster-weight 
. More precisely, we will explain how one derives crossing estimates in quads which are uniform in their boundary conditions and depend only on the extremal lengths of the quads. These estimates have important consequences concerning the sub-sequential scaling limits of the collection of interfaces between primal and dual clusters, arm-exponents, quasi-multiplicativity, etc.
This is a joint work with Ioan Manolescu and Vincent Tassion.