Mathematical Sciences: Geometric Group Theory

这个项目是关于树的理论 格和格作用于树的zeta函数。 首席研究员将探索格子在 局部有限一致树的自同构群 的 数学问题涉及格，体积， 可扩展性类、zeta函数和光谱 理论 一个格是一组对象和一个顺序 在这些物体上，任何一对物体都有一个 最大下界和最小上界。 晶格具有 在李群的研究中非常有用。 中 类似的精神，这个项目将探索格子在 某些树的自同构群 这项工作是 对数学的许多不同领域感兴趣。 它还 在信息论中有潜在的应用。

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.