题目：Approximation on the Voronoi Cells of the A_d Lattice

报告人：Professor Xingping Sun

　　　Department of Mathematics，Missouri State University

时间：2010年8月26日（星期四）上午 10:00-10:45

地点：软件所5号楼337会议室

摘要：

The Voronoi cells of the A_d lattice are interesting geometric objects. For examples, the Voronoi cells of A_2 are regular hexagons, and those of A_3 are rhombic dodecahedrons. The two lattices A_2 and A_3 give best packing in R^2 and R^3, respectively. For all d, the Voronoi cells can be expressed as unimodular zonotopes, i.e., zonotopes that have (d + 1) generators. They contain discrete subgroups induced by sublattices of A_d. These subgroups are abelian and the interactions between these groups and their dual groups provide a fertile field for doing discrete Fourier analysis akin to the fast Fourier transform done on the unit circle. This naturally leads us to study many interesting approximation problems on the Voronoi cells. The group structure and the zonotopal algebra play very important roles in the proof of many interesting results, such as finding compact formulas for the Dirichlet and Fejer kernels. Some open questions will be presented.