Theorems of Brion, Lawrence, and Varchenko on rational generating functions for cones

Polar decomposition and Brion's theorem

In this note we point out the relation between Brion's formula for the lattice point generating function of a convex polytope in terms of the vertex cones [Brion1988] on the one hand, and the polar decomposition à la Lawrence/Varchenko [Lawrence1991, Varchenko1987] on the other. We then go on to prove a version of polar decomposition for non-simple polytopes.

论Arthur迹公式的组合学、凸多面体与环面簇

On Combinatorics of the Arthur Trace Formula, Convex Polytopes, and Toric Varieties

本文从扇与多面体出发构造组合截断函数，证明其积分的收敛性与多项式性，推广了Arthur迹公式、Ehrhart多项式及Langlands引理，并给出环面簇上的几何解释。