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.

该奖项支持参加会议“有限简单团体：Atlas及以后的30年”，于2015年11月2日至5日在新泽西州普林斯顿的普林斯顿大学举行。数学群体的概念是从对称的概念中得出的。对象在自然或科学中的对称性是由一个组编码的，该组传递了有关对象本身结构的重要信息。小组理论在物理和化学中有许多重要的应用，尤其是在量子力学和基本颗粒理论中。会议的主要主题是理论与计算之间的相互作用，以及小组理论在其他数学领域的应用。邀请参与者的名单是来自这些领域的高级和初级研究人员，因此会在会议期间和之后促进他们之间的进一步互动和协作。会议活动将包括该领域专家组织的非正式工作组，讨论会议期间的当前和未来研究指示；海报会议；网页；和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.该策略利用有关有限简单组的信息，其中一些是在“有限群体的地图集”和“ Brauer字符的地图集”中分类的。在许多当代数学领域的研究人员的日常生活中，地图集和相关计算机代数系统的作用是不可能高估地图集的作用。 该会议将汇集一群在群体理论，代表理论和计算群体理论方面的研究人员。会议的目的是讨论地图集的众多应用，并探讨最新的发展和未来研究方向。