|Location:||MSRI: Baker Board Room|
The sine-Gordon Y-systems and the reduced sine-Gordon Y-systems were introduced by Roberto Tateo in 90\'s in the study of the integrable deformation of the minimal models in conformal field theory by the thermodynamic Bethe ansatz method.
They are associated to continued fractions, and the periodicity property of these Y-systems was conjectured by Tateo; however, it has been only partially proved so far.
We prove the periodicity in full generality using the surface method of cluster algebras.
It turns out that there is a wonderful interplay among continued fractions, triangulations, cluster algebras, and Y-systems, which I would like to explain in this talk.
This is a joint work with Salvatore Stella.