Categorical Lie algebra actions, quiver varieties, and braid group actions -- Joel Kamnitzer, November 6, 2009

I will discuss the notion of categorical Lie algebra actions, as introduced by Rouquier and Khovanov-Lauda. In particular, I will give examples of categorical Lie algebra actions on derived categories of coherent sheaves on quiver varieties. These categorical Lie algebra actions lead to actions of braid groups, generalizing known actions by spherical twists. I will explain applications to constructions of knot homology theories and connections to symplectic geometry.