MaPhySto
The Danish National Research Foundation:
Network in Mathematical Physics and Stochastics

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Funded by The Danish National Research Foundation

Geometric Mathematical Physics Seminar

Abstract
It will be explained how to derive a wide class of classical integrable systems (the so-called Hitchin systems) starting with a simplified version of the Chern-Simons theory. These theories are described by the Hamiltonian systems defined on the Higgs bundles over Riemann curves. The Lax representation, conservation laws, spectral curves and the action-angle variables are the natural ingredients of this construction. The case of the genus one curves will be elaborated in details. It leads to the integrable many-body problem of Calogero-Moser type and to the integrable elliptic tops related to generalized XYZ spin chains.

Contact person:Jørgen Ellegaard Andersen.