Geometry and dynamics of integrable systems with extended supersymmetry

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The project focuses on integrable systems which possess additional symmetries such as conformal symmetry or/and extended supersymmetry. New multi-particle rational, trigonometric and hyperbolic Calogero systems associated with the A(n), B(n), C(n) and D(n) Lie algebras with an arbitrary even number of supersymmetries will be constructed and analyzed within the Hamiltonian approach. The superconformal symmetries of these models will be visualized by an explicit construction of the corresponding conserved currents. Calogero systems associated with the exceptional G(2) and F(4) algebras and possessing N-extended supersymmetry will be constructed and analyzed. A superfield description of these models with N=2 and N=4 supersymmetry will be provided. For a large class of integrable models, N=2 and N=4 supersymmetric extensions will be constructed and investigated. This includes Ruijsenaars-Schneider systems, Schwarzian mechanics, Euler, Lagrange, Kovalevskaya and Goryachev-Chaplygin tops, multi-vortices on the plane, and su(2) mechanics associated with the angular sector of a relativistic spinning particle on a spherically symmetric gravitational background.