Mathematical Sciences\RUI: Problems in Algebra: Group Actions on Trees and Buildings

9623282 Alperin这笔赠款支持R.Alperin教授致力于各种几何对象上有限群表示问题的研究。特别是，他想研究作用于树木、建筑及其泛化的群体。他希望利用各种不动点性质来帮助对具有各种同调或几何实现的某些群进行分类。这是群论领域的研究。群论可以被认为是对抽象对称性的研究。因此，这个领域在物理和化学的许多领域都有直接的应用。此外，在过去的30年里，使用群论的技术解决了许多与数据传输中的问题有关的问题。还有与纠错码的直接连接，这些纠错码对现代计算至关重要，例如与CD-ROM一起工作。

9623282 Alperin This grant supports the research of Professor R. Alperin to work on problems in the representation of finite groups on various geometric objects. In particular he wants to work on groups acting on trees, buildings and their generalizations. He hopes to use various fixed point properties as an aid in classifying certain groups with various homological or geometrical realizations. This is research in the field of group theory. Group theory can be thought of as the study of symmetry in the abstract. As such, this area has direct applications to many areas of physics and chemistry. Moreover, within the last 30 years, many connections to problems in data transmission have been solved using techniques from group theory. There are also direct connections to the error correcting codes that are vital for modern computing such as working with CD-ROM's.