Abstract:
This talk evolves around so-called fully-packed loop configurations. The Razumov-Stroganov conjecture relates enumerative properties of such objects to the stationary distribution of a Markov chain appearing in the context of certain integrable quantum systems. Very recently, Luigi Cantini and Andrea Sportiello gave a proof of the conjecture. The purpose of the talk is to explain the main ideas of the proof. Much focus will be on the dihedral symmetry of loop configurations exposed in previous work by Benjamin Wieland; the proof of the conjecture relies heavily on this symmetry. I will not assume any previous knowledge of loop configurations.