Szenes András: The Y-system
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Abstract:

In 1991, Zamolodchikov discovered an intriguing rational recursion called
the Y-system. There is a Y-system for every graph, and one can show that 
the
recursion is periodic if and only if the graph is a Dynkin diagram.
The Y-systems gave rise to identities among the values of the dilogarithm
function, and also served as one of the first examples of an important new
notion of modern algebra: the cluster algebras. In this talk, we will 
review
recent results and developments in the field.