Mathematical Sciences: Geometric Group Theory

这个项目是关于树格的理论和作用在树上的格的Zeta函数。主要研究人员将探索局部有限一致树的自同构群中的格。数学问题涉及到格子、体积、可公度类、Zeta函数和谱理论的存在。晶格是一组对象以及这些对象上的顺序，使得任何一对对象都具有最大的下界和最小的上界。格子已被证明在李群的研究中非常有用。本着类似的精神，这个项目将探索某些树的自同构群中的晶格。这项工作对数学的许多不同领域都很有意义。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.