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

## Lagrangians, symplectomorphisms and zeroes of moment maps

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.

### Date & Time

April 08, 2022 | 9:15am – 10:45am

Remote Access

Yann Rollin

### Speaker Affiliation

Nantes University