Quantum integrability and Combinatorics: qKZ, ASM, PP

Abstract:

We shall review the recent progress, based on the use of the quantum Knizhnik-Zamolodchikov equation, on the integrable model of loops which is the subject of the Razumov-Stroganov conjecture. Then we shall present some applications to enumerative combinatorics, settling in particular some old conjectures on Alternating Sign Matrices and Plane Partitions.