During the last decades\, important pr ogresses have been made concerning the computation of form factors and correlation functions of simp le models solvable by algebraic Bethe Ansatz (ABA) such as the XXZ spin-1/2 chain or 1D Bose gas wit h periodic boundary conditions. However\, the gene ralization of these results to more complicated mo dels or different types of integrable boundary con ditions is for the moment limited by the range of applicability of ABA or by some difficulties of th e method.

In this talk\, we discuss t he solution of Heisenberg spin chains (XXX\, XXZ o r XYZ) in the framework of a complementary approac h\, Sklyanin'\;s quantum Separation of Variable s approach. This enables us notably to consider fo r these models various types of boundary condition s (quasi-periodic\, open...) not directly solvable by Bethe ansatz. More precisely\, we discuss in t his framework some new results and open problems c oncerning the description of the spectrum by means of solutions of a functional T-Q equation (or equ ivalently in terms of Bethe-type equations). We al so discuss the problem of the computation of the e igenstates scalar products and of the form factors of local operators. LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR