Mathematical Sciences: Research in Representation Theory andAutomorphic Forms

Wallach将研究作用在约化李代数上的不变分布上的不变微分算子、Coxeter群的对角不变量和调和、与格点问题渐近行为中的误差项有关的自同构形式以及Klosterman-Selberg Zeta函数。Wallach还将致力于开发计算Groebner基的并行计算机算法，以及用于研究Coxeter群的对角不变量和调和的通用软件包。李群理论是以挪威数学家索菲斯·李的名字命名的，一直是20世纪数学的主要主题之一。作为利用系统固有对称性的数学工具，李群的表示理论对数学本身，特别是在分析和数论方面，以及对理论物理，特别是量子力学和基本粒子物理，都产生了深远的影响。

Wallach will investigate invariant differential operators acting on invariant distributions on a reductive Lie algebra, diagonal invariants and harmonics for Coxeter groups, Automorphic forms related to the error term in asymptotic behavior of lattice point problem and the Kloosterman-Selberg zeta function. Wallach will also work to develop parallel computer algorithms for the calculation of Groebner bases and a general software package to be used in the study of diagonal invariants and harmonics for Coxeter groups. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.