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.
