Hilbert functions of multigraded algebras, mixed multiplicities of   ideals and their applications
  This paper is a survey on major results on Hilbert functions of multigraded algebras and mixed multiplicities of ideals, including their applications to the computation of Milnor numbers of complex analytic hypersurfaces with isolated singularity, multiplicities of blowup algebras and mixed volumes of polytopes. 
N. V. Trung and J. K. Verma