Homological stability for symmetric complements
  Conjecture F from [VW12] states that the complements of closures of certain strata of the symmetric power of a smooth irreducible complex variety exhibit rational homological stability. We prove a generalization of this conjecture to the case of connected manifolds of dimension at least 2 and give an explicit homological stability range. 
Alexander Kupers, Jeremy Miller, TriThang Tran
math.AT math.AG