Geometric construction of semicanonical bases and crystals of (affine) Lie algebras via quivers and Higgs bundles

In this talk I will present the construction of enveloping Lie algebras via constructible fonctions on a stack of representation of a quiver (by Lusztig), as well as the geometric construction of the crystal (by Kashiwara-Saito).
I will then present how this techniques can be translated in the framework of Higgs bundles on a curve, in order to obtain loop Lie algebras.