Physics and combinatorics around the Razumov-Stroganov correspondence

Thursday 3 Mar 2016, 16:15 → 17:15 Europe/Brussels

CYCL01 (Marc de Hemptinne)

Luigi Cantini (Université de Cergy-Pontoise, France)

Summary :

 

In 2001, Razumov and Stroganov put forward a conjecture that immediately intrigued both physicist and combinatorialists. 
They conjectured that the (properly normalized) components of the ground state of a statistical physics model, called "dense O(1) loop model”, enumerate fully-packed loop configurations on the square, refined according to the link pattern for the boundary points. 
In this talk, after introducing some background and explaining the Razumov-Stroganov correspondence, I'll discuss its relations with several important questions in enumerative combinatorics and in the theory of quantum integrable system, and I'll explain the main tool that has led to its proof.