Finite Simple Groups: Thirty Years of the Atlas and Beyond

有限简单群：阿特拉斯三十年及以后

• 批准号: 1455798
• 负责人: Pham Tiep
• 金额: $ 3.99万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-07-01 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1455798&HistoricalAwards=false
• 关键词: Finite; Simple; Groups; Thirty; Years

This award supports participation in the conference "Finite Simple Groups: Thirty Years of the Atlas and Beyond" taking place November 2-5, 2015, at Princeton University in Princeton, NJ. The concept of a group in mathematics grew out of the notion of symmetry. The symmetries of an object in nature or science are encoded by a group, and this group carries important information about the structure of the object itself. Group theory has had many important applications in physics and chemistry, particularly in quantum mechanics and in the theory of elementary particles. The main theme of the conference will be the interaction between theory and computation, and applications of group theory to other areas of mathematics. The list of invited participants features senior and junior researchers from across these fields and thus will foster further interaction and collaboration between them, during and after the conference. Conference activities will include informal working groups organized by experts in the field to discuss current and future research directions during the conference; a poster session; a webpage; and a wiki. The proceedings of the conference will be published.The classification of finite simple groups, one of the most monumental accomplishments of the modern mathematics, was announced to be completed in 1983. Since then, it has opened up a new and powerful strategy to approach and resolve many, previously inaccessible problems in group theory, number theory, combinatorics, coding theory, algebraic geometry, and other areas of mathematics. This strategy utilizes information about finite simple groups, some of which is catalogued in the "Atlas of Finite Groups" and "An Atlas of Brauer Characters." It is impossible to overestimate the roles of the atlases and the related computer algebra systems in everyday life of researchers in many areas of contemporary mathematics. The conference will bring together a diverse group of researchers in group theory, representation theory, and computational group theory. The objective of the conference is to discuss numerous applications of the Atlases and to explore recent developments and future directions of research.

该奖项支持参加2015年11月2日至5日在新泽西州普林斯顿大学举行的“有限简单群：阿特拉斯三十年及以后”会议。数学中群的概念是从对称性的概念发展而来的。在自然界或科学中，物体的对称性是由一个群编码的，这个群携带着关于物体本身结构的重要信息。群论在物理学和化学中有许多重要的应用，特别是在量子力学和基本粒子理论中。会议的主题将是理论和计算之间的相互作用，以及群论在数学其他领域的应用。受邀与会者名单包括来自这些领域的高级和初级研究人员，因此将在会议期间和之后促进他们之间的进一步互动和合作。会议活动将包括由该领域专家组织的非正式工作组，讨论会议期间当前和未来的研究方向;海报会议;网页和维基。有限单群的分类是现代数学最伟大的成就之一，它将于1983年完成。从那时起，它开辟了一个新的和强大的战略，以接近和解决许多，以前无法解决的问题，在群论，数论，组合数学，编码理论，代数几何，和其他领域的数学。这种策略利用了有限单群的信息，其中一些在《有限群图集》和《布劳尔特征标图集》中被编目。“地图集和相关计算机代数系统在当代数学许多领域的研究人员日常生活中的作用是不可能高估的。 会议将汇集一组不同的研究人员在群论，表示理论和计算群论。会议的目的是讨论酶的许多应用，并探讨最近的发展和未来的研究方向。