Modular Representations of Finite Groups, Codes and Projective Geometry Over Finite Fields

9701065 Sin该奖项为一个研究项目提供资金，该项目位于三个领域的交叉点，有限群的模块化表示，有限射影几何和设计理论及其规范。在这个项目中，他将尝试一方面建立一个通用的框架，在这个框架中，表示理论和群上同的技术可以应用于解决关于编码和几何的组合问题，另一方面，他将研究后者如何在表示理论中提供更几何的观点。这项研究的成功结果将导致所有三种理论的新方法和新结果，最重要的是，它们之间的思想相互交融。这项研究属于组合学的一般领域。组合学的目标之一是找到研究离散对象集合如何排列的有效方法。离散系统的行为对现代通信极为重要。例如，大型网络的设计，比如那些出现在电话系统中的网络，以及计算机科学中处理离散对象集的算法设计，这就利用了组合研究。

9701065 Sin This award provides funding for a research project that lies at the intersection of three areas, modular representations of finite groups, finite projective geometry and the theory of designs and their codes. Under this project, Sin will try to on the one hand build a general framework in which techniques of representation theory and group cohomology can be applied to attack combinatorial problems about codes and geometries, while on the other hand he will study how the latter areas may provide a more geometric viewpoint in representation theory. The successful outcome of this research should lead to new methods and results in all three theories and, above all, to a cross-fertilization of ideas among them. This research is in the general area of Combinatorics. One of the goals of Combinatorics is to find efficient methods of studying how discrete collections of objects can be arranged. The behavior of discrete systems is extremely important to modern communications. For example, the design of large networks, such as those occurring in telephone systems, and the design of algorithms in computer science deal with discrete sets of objects, and this makes use of combinatorial research.