We construct completely integrable torus actions on the dual Lie algebra of any compact Lie
group $ K $ with respect to the standard Lie-Poisson structure. These systems generalize …

Coadjoint orbits and multiplicity free spaces of compact Lie groups are important examples
of symplectic manifolds with Hamiltonian groups actions. Constructing action-angle …

Let G be a connected semisimple Lie group. There are two natural duality constructions that
assign to G: its Langlands dual group G^ ∨ G∨, and its Poisson–Lie dual group G^* G∗ …

In this thesis, we study Poisson geometry and representation theory by using the approach
of geometrization and tropicalization. The goal is to find relations between some new …

The main contribution of this manuscript is a local normal form for Hamiltonian actions of
Poisson–Lie groups K on a symplectic manifold equipped with an A N-valued moment map …

I present three papers written on the theme of the interaction between polyhedra and Hamil-
tonian mechanics. In the first, I extend Delzant's classification of toric symplectic mani-folds …