Geometric Methods in Group Theory

9401627 BASS该奖项支持使用几何方法研究群论中的一些问题。主要研究人员将致力于简化群表示的平坦族的线性化；区间动力学中的重整化和有根树的自同构群；计算单纯树作用的外自同构群中的双曲长度函数的稳定器；发展非均匀树格理论；以及有限生成群表示理论中的几个主题。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。

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.