Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

I will present two constructions of Kähler manifolds, endowed with Hamiltonian torus actions of infinite dimension. In the first example, zeroes of the moment map are related to isotropic maps from a surfaces in $\mathbb{R}^{2n}$. In the second example, which is actually a hyperKähler moment map, the zeroes are related to symplectic maps of the torus $T^{4}$. The corresponding modified moment map flows have short time existence. Polyhedral analogues of these constructions can be used to investigate piecewise linear symplectic geometry.