New action-angle variables on coadjoint orbits

GAP Seminar

Meeting Details

For more information about this meeting, contact Allyson Borger, Nigel Higson, Ping Xu, Mathieu Stiénon.

Speaker: Yanpeng Li, University of Geneva

Abstract: The problem of constructing global action-angle variables on coadjoint orbits of compact Lie groups is one of the interesting questions in the theory of integrable systems. A fundamental contribution was made by Guillemin-Sternberg who constructed the Gelfand-Zeitlin integrable systems on coadjoint orbits of the groups SU(n) and SO(n). Recently, toric degeneration techniques allowed for the construction of global action-angle variables on rational coadjoint orbits of compact Lie groups of all types. In this talk, I will present a new approach which aims at constructing global action-angle coordinates on all regular coadjoint orbits of compact Lie groups and on a large family of related Hamiltonian spaces. It combines the results of Ginzburg-Weinstein on the theory of Poisson-Lie groups and the theory of cluster algebras using the "partial tropicalization'' procedure. The talk is based on joint works with A. Alekseev, A. Berenstein, B. Hoffman, and J. Lane.

Room Reservation Information

Room Number: 106 McAllister

Date: 09/24/2019

Time: 2:30pm - 3:30pm