New polytope decompositions and Euler-Maclaurin formulas for simple   integral polytopes
  We use a version of localization in equivariant cohomology for the norm-square of the moment map, described by Paradan, to give several weighted decompositions for simple polytopes. As an application, we study Euler-Maclaurin formulas. 
Jose Agapito and Leonor Godinho