The Soergel category and the redotted Webster algebra
  We describe a collection of graded rings which surject onto Webster rings for sl(2) and which should be related to certain categories of singular Soergel bimodules. In the first non-trivial case, we construct a categorical braid group action which categorifies the Burau representation. 
Mikhail Khovanov and Joshua Sussan
math.QA math.GT math.RT