权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

New directions in noncommutative geometry.

非交换几何的新方向。

基本信息

批准号：
EP/G012296/1
负责人：
Jacek Brodzki
金额：
$ 1.41万
依托单位：
University of Southampton
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2008
资助国家：
英国
起止时间：
2008 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FG012296%2F1
关键词：
New directions noncommutative geometry.

项目摘要

We propose to hold a workshop in a very active and exciting area of modern pure mathematics, which is known as noncommutative geometry. A fundamental premise of noncommutative geometry is the idea that thatinformation about a space or a group can be obtained from properties of a suitable operator algebra. For a group G, an example of an interesting space to consider is a space of its irreducible representations. These spaces typically have a very complicated structure and various topological tools have been developed to assist in their study.Another way to understand the representation theory of a group is through the study of associated group C*-algebras, which according to the philosophy of noncommutative geometry, play the role of the algebras of continuous functions of spaces of irreducible representationsof the group. For example, the reduced C*-algebra of a group contains information about the irreducible representations of the group G that make up theleft regular representation of G.The Baum-Connes conjecture proposes a scheme of extracting topological information about the space of representations of a group by means of K-theory of its reduced C*-algebra. This hypothesis links in a very ingenious way analytic properties of the group with the geometry of spaces on which it acts in a prescribed way. This conjecture has been the subject of intense study over the past two decades and has produced a number of wonderful results. Some of the most exciting insights that emerged recently is the link between the conjecture and the Langlands programme, which is a sophisticated scheme that describes the structure of spaces of representations of a certain class of groups. Our workshop will bring together leading mathematicians to provide an excellent opportunity for the exchange of ideas that are likely to lead to the resolution of a number of interesting and difficult problems in this area. It is rare that the speakers invited to our meeting are present in the UK at the same time.

我们提议在现代纯数学中一个非常活跃和令人兴奋的领域，即非交换几何，举办一个研讨会。非交换几何的一个基本前提是关于一个空间或群的信息可以从一个合适的算子代数的性质中得到。对于群G，一个值得考虑的有趣空间的例子是其不可约表示的空间。这些空间通常具有非常复杂的结构，并且已经开发了各种拓扑工具来帮助研究它们。另一种理解群的表示理论的方法是通过研究关联群C*-代数，根据非交换几何的哲学，它扮演了群的不可约表示空间的连续函数代数的角色。例如，群的约简C*-代数包含了构成G的左正则表示的群G的不可约表示的信息。Baum-Connes猜想提出了一种利用群的约简C*-代数的k理论提取群的表示空间拓扑信息的方案。这个假设以一种非常巧妙的方式将群的解析性质与它以规定方式作用的空间的几何形状联系起来。在过去的二十年里，这一猜想一直是人们激烈研究的主题，并产生了许多奇妙的结果。最近出现的一些最令人兴奋的见解是这个猜想和朗兰兹纲领之间的联系，朗兰兹纲领是一个复杂的方案，描述了某一类群体的表征空间结构。我们的研讨会将汇集顶尖的数学家，为交流思想提供一个极好的机会，这些思想很可能导致解决这个领域的一些有趣和困难的问题。我们这次会议邀请的演讲者同时在英国，这是很罕见的。