Dr Maxime Fairon - Geometric reductions of spin trigonometric RS systems
he Ruijsenaars-Schneider (RS) system is a celebrated integrable system, which describes the motion of interacting particles that are invariant under Poincaré transformations. In 1995, it was realised by Krichever and Zabrodin that the system admits a spin generalisation, where the particles are endowed with internal 'spin' degrees of freedom.
My goal is to review the story of the quasi-Hamiltonian reduction of such systems in the presence of a trigonometric potential following a joint work with Chalykh (in the complex case) and a current investigation with Fehér (in the real case). I will also outline the parallel Hamiltonian reduction with Poisson-Lie symmetry due to Arutyunov and Olivucci (in the complex case), or due to Fehér, Marshall and myself (in the real case).
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