April 28, 2010
Jakob Jonsson (KTH): The Cantini-Sportiello proof of the Razumov-Stroganov conjecture
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.