Workshop: Themes at the interface of Physics and Algebraic Representation Theory

研讨会：物理与代数表示论界面的主题

• 批准号: EP/E021328/1
• 负责人: Paul Martin
• 金额: $ 1.81万
• 依托单位: City, University of London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2006
• 资助国家: 英国
• 起止时间: 2006 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FE021328%2F1
• 关键词: Workshop; Themes; interface; Physics; Algebraic

Whilst abstract mathematics often manifests structures of great beauty, and also of great use in practical applications, some of the most beautiful and powerful structures of all have come from the tight integration of mathematics as a self-consistent model of the physical world. For example, diagram algebras are, in one sense, abstract algebras, but they are also rather direct models of algebraic structures which can be seen in the physical world (from the connectivity of integratedcircuits, to the phase transitions in ferromagnetic materials). In them, powerful and elegant abstract mathematical techniques have a very concrete realisation, and very close cooperation with physicalinsight. This workshop is intended to bring together several world leaders in fields exemplified by this paradigm, with experts in physical world systems of present or potential application, as well as promising young researchers from both sides. The aim is to take full stock of, and coordinate, progress so far, and to drive forward work in this exciting confluence of mathematics and physics.

虽然抽象的数学经常表现出非常美丽的结构，在实际应用中也非常有用，但其中一些最美丽和最强大的结构来自于数学作为物理世界的自洽模型的紧密结合。例如，图代数在某种意义上是抽象的代数，但它们也是在物理世界中可以看到的代数结构的相当直接的模型(从集成电路的连通性到铁磁材料中的相变)。在它们当中，强大而优雅的抽象数学技巧有非常具体的实现，并与物理洞察力有非常密切的合作。这次研讨会的目的是让这一范例领域的几位世界领袖、现有或潜在应用的物理世界系统方面的专家以及来自双方的有前途的年轻研究人员聚集在一起。其目的是充分评估和协调到目前为止的进展，并在这一令人兴奋的数学和物理的交汇处推动工作向前发展。

项目成果

Higher-dimensional Temperley-Lieb algebras

高维 Temperley-Lieb 代数

• DOI: 10.1088/1751-8113/40/38/f01
• 发表时间: 2007
• 期刊: Mathematical and Theoretical
• 作者: Alvarez M

On the blocks of the walled Brauer algebra

• DOI: 10.1016/j.jalgebra.2008.01.026
• 发表时间: 2007-09
• 期刊: Journal of Algebra
• 影响因子: 0.9
• 作者: A. Cox;M. Visscher;S. Doty;Paul Martin

Constructing cell data for diagram algebras

构建图代数的单元数据

• DOI: 10.1016/j.jpaa.2006.07.016
• 发表时间: 2007
• 期刊: Journal of Pure and Applied Algebra
• 影响因子: 0.8
• 作者: Green R

Towers of recollement and bases for diagram algebras: Planar diagrams and a little beyond

图代数的重整塔和基础：平面图及更多

• DOI: 10.1016/j.jalgebra.2007.04.013
• 发表时间: 2007
• 期刊: Journal of Algebra
• 影响因子: 0.9
• 作者: Martin P