| Résume | I will present two expository lectures on the work of Maulik and Okounkov (\href{}{http://arxiv.org/abs/1211.1287}), focusing on the geometric R-matrix formalism which leads to the construction of a Hopf algebra $Y_Q$ acting on the equivariant cohomology of the Nakajima varieties associated to a quiver $Q$.
In the first lecture, I will give an overview of the stable basis construction in the equivariant cohomology of an algebraic symplectic variety, which is the key technical tool used to construct the geometric R-matrices. I will then present an explicit example of the Maulik-Okounkov construction in the simple case of cotangent bundles to Grassmannians, which will yield a geometric construction of the Yangian of $gl_2$. |
