On the Periodicity Conjecture for Y-systems
Alexander Volkov
Y-systems are a certain family of algebraic recurrence equations,
which in their present form emerged in the early 1990s in the study of
the Thermodynamic Bethe Ansatz. They are naturally associated to
arbitrary pairs of Dynkin diagrams, and the periodicity conjecture
asserts that all solutions to those systems are periodic with period
equal to twice the sum of the respective Coxeter numbers. Although
this conjecture has by now been largely proved, there remain open
questions. In this talk, I will discuss an approach to the topic based
on the generalized Liouville formula, and present some recent
developments..