# CMSA Geometry and Physics Seminar: Collective integrable systems and global action-angle coordinates

CMSA EVENTS

##### Speaker:

Jeremy Lane *- McMaster University*

A "collective integrable system" on a symplectic manifold is a commutative integrable system constructed from a Hamiltonian action of a non-commutative Lie group. Motivated by the example of Gelfand-Zeitlin systems, we give a construction of collective integrable systems that generate a Hamiltonian torus action on a dense subset of any Hamiltonian K-manifold, where K is any compact connected Lie group. In the case where the Hamiltonian K-manifold is compact and multiplicity free, the resulting Hamiltonian torus action is completely integrable and yields global action angle coordinates. Moreover, the image of the moment map is a (non-simple) convex polytope.

Zoom: https://harvard.zoom.us/j/94717938264