We consider n× n systems of linear ODEs on P 1 with a regular singularity at z= 0 and an
irregular singularity of rank 1 (double pole) at z=∞. The monodromy data of such a system …

Langlands duality is one of the most influential topics in mathematical research. It has many
different appearances and influential subtopics. Yet there is a topic that until now seems …

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

For a compact Poisson-Lie group $ K $, the homogeneous space $ K/T $ carries a family of
symplectic forms $\omega_\xi^ s $, where $\xi\in\mathfrak {t}^* _+ $ is in the positive Weyl …

Let G be a connected and simply connected complex semisimple Lie group. For a collection
of homogeneous G-spaces G/Q, we construct a finite atlas A _\scriptscriptstyle BS (G/Q) A …

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 …

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 …