Hamiltonian reduction and duality in integrable systems

The objective of my talk is to explain the notion of duality for integrable systems, and to see how it emerges naturally out of the procedure of Hamiltonian reduction. The general family of integrable systems of interest here includes the original Calogero model, and those of Sutherland, Ruijsenaars and Schneider. If all goes well, my aim will to present a couple of systems in duality with one another. One of these was obtained by me about ten years ago: it is a system of Ruijsenaars type analogous to the $\mathrm{BC}_n$ Sutherland model, discovered by Olshanetsky and Perelomov in 1976. The other system is new.