We, Tomasz Przezdziecki and Ben Davison, are planning a reading seminar on braid group actions on categories. The rough plan is that we start off with the Seidel-Thomas paper
"Braid group actions on derived categories of coherent sheaves" https://arxiv.org/abs/math/0001043
and take it from there, with an eye on algebraic geometry as well as representation theory. The two papers we will aim at understanding by the end of the seminar (spending roughly half the remaining time on each) are
Bezrukavnikov+Riche: "Affine braid group actions on derived categories of Springer resolutions" https://arxiv.org/abs/1101.3702
Cautis+Kamnizer+Licata: "Coherent Sheaves on Quiver Varieties and Categorification" https://arxiv.org/abs/1104.0352
Our aim is to not assume a great deal of representation theory or algebraic geometry - so for instance we'll be reviewing things like Nakajima's Lie algebra actions on cohomology of quiver varieties, and other requisite background.
The structure is still somewhat open; if this is something you'd be interested in taking part in, or if you have any suggestions regarding structure/material, please let us know.