Approximate subgroups
  Given a definably amenable approximate subgroup $A$ of a (local) group in some first-order structure, there is a type-definable subgroup $H$ normalised by $A$ and contained in $A^4$ such that every definable superset of $H$ has positive measure. 
Jean-Cyrille Massicot, Frank Olaf Wagner (ICJ)
math.LO