Finite Simple Groups: Thirty Years of the Atlas and Beyond

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普林斯顿大学举行的“有限简单群体：地图集的三十年及以后”会议。数学中的群的概念起源于对称性的概念。自然界或科学中一个物体的对称性是由一个组编码的，而这个组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论中。会议的主题将是理论和计算之间的互动，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，因此将促进他们在会议期间和之后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，在会议期间讨论当前和未来的研究方向；一次海报会议；一个网页；以及一个维基。会议纪要将公布。有限单群的分类是现代数学最不朽的成就之一，于1983年宣布完成。从那时起，它开辟了一种新的强大的策略来接近和解决群论、数论、组合学、编码论、代数几何和其他数学领域中许多以前无法解决的问题。这一策略利用了有关有限单群的信息，其中一些被编目在《有限群图集》和《布劳尔人物图集》中。在当代数学的许多领域，地图集和相关的计算机代数系统在研究人员的日常生活中的作用怎么估计都不为过。这次会议将汇聚群论、表象理论和计算群论领域的不同研究人员。会议的目的是讨论地图集的许多应用，并探讨最近的发展和今后的研究方向。

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.