Geometric Methods in Group Theory

9401627 Bass This award supports research on a number of questions in group theory using geometric methods. The principal investigator will work on linearizing flat families of reductive group representations; renormalization in interval dynamics and automorphism groups of rooted trees; calculating the stabilizer, in the outer automorphism group, of the hyperbolic length function of a simplicial tree action; developing the theory of non-uniform tree lattices; and several topics in the representation theory of finitely generated groups. 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.