The Congruence Subgroup Problem and Groups of Finite Representation Type

小行星9700474 该奖项提供资金，继续的同余子群问题的S-算术子群的线性代数群在数域。主要研究者将尝试使用各种技术，如不同的有界性条件（有界生成和类似性质），表示论的方法（Kazhdan的性质（T））等，来证明一些新类别的群的同余核的中心性，他还将研究具有有限表示类型的群的性质和一些有限生成群的表示变体。 本文的研究属于数论中的一般数学领域福尔斯。 数论有其历史根源，在研究整个数字，解决这样的问题，如那些处理整除一个整数由另一个。它是数学中最古老的分支之一，几个世纪以来，人们纯粹出于美学的原因而追求它。然而，在过去的半个世纪，它已成为一个不可或缺的工具，在不同的应用领域，如数据传输和处理，通信系统。

9700474 Rapinchuk This award provides funding for a continuing of the congruence subgroup problem for S-arithmetic subgroups of linear algebraic groups over number fields. The principal investigator will attempt to prove the centrality of the congruence kernel for some new classes of groups using a variety of techniques such as different boundedness conditions (bounded generation and similar properties), methods of representation theory (property (T) of Kazhdan), etc. He will also study the properties of groups having finite representation type and the representation varieties of some finitely generated groups. This research falls into the general mathematical field of Number Theory. Number Theory has its historical roots in the study of the whole numbers, addressing such questions as those dealing with the divisibility of one whole number by another. It is among the oldest branches of mathematics and was pursued for many centuries for purely aesthetic reasons. However, within the last half century it has become an indispensable tool in diverse applications in areas such as data transmission and processing, and communication systems.