Mathematical Sciences: Geometric Group Theory

这个项目是关于树格的理论和作用于树的格的ζ函数。主要研究者将研究局部有限一致树的自同构群中的格。数学问题涉及格、体积、可通约性类、ζ函数和谱理论的存在性。格是一组对象的集合，在这些对象上有一个顺序，使得任何一对对象都有一个最大下界和最小上界。格在李群的研究中被证明是非常有用的。本着类似的精神，这个项目将探索某些树的自同构群中的格。这项工作引起了许多不同数学领域的兴趣。它在信息论中也有潜在的应用。

This project is concerned with the theory of tree lattices and zeta functions for lattices acting on trees. The principal investigator will explore lattices in the automorphism group of a locally finite uniform tree. The mathematical issues concern existence of lattices, volumes, commensurability classes, zeta functions, and spectral theory. A lattice is a set of objects together with an order on these objects such that any pair of objects has a greatest lower bound and a least upper bound. Lattices have shown to be quite useful in the study of Lie groups. In a similar spirit this project will explore lattices in the automorphism group of certain trees. This work is of interest to many different areas of mathematics. It also has potential applications in information theory.