Conformal harmonic maps of two-torus to spheres and turning point of elliptic Calogero–Moser system

The theory of harmonic maps of Riemann surfaces to spheres is a classical problem of differential geometry. In this talk we present a construction for conformal harmonic maps of two-dimensional torus to spheres of arbitrary dimensions, which are multidimensional generalizations of instanton maps of two-dimensional torus to two-dimensional sphere. The crucial point of our construction is based on surprising relation of the problem to the theory of elliptic Calogero–Moser system. The talk is based on the joint paper with Nikita Nekrasov.

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