In 2001 Razumov and Stroganov conjectured that the (properly normalized) components of the ground state of the dense O(1) loop model on a semi-infinite cylinder enumerate fully-packed loop (FPL) configurations on the square, with alternating boundary conditions, refined according to the link pattern for the boundary points. This conjecture has arisen a lot of interest both in the physics and in the mathematics community. par In this talk, after reviewing the main background, I will present a proof of this conjecture. The main idea is to recognize the fundamental role of “gyration”, an operation that can be performed on FPL, which was already the key in Wieland’s proof of the rotational symmetry of the FPL enumerations.

LPT-ENS