Simple groups, representations, and related topics

“简单群、表示和相关主题”会议将于2015年7月13日至15日在英国剑桥大学数学科学中心举行。该基金部分支持美国研究人员，特别是早期职业数学家参加这个主要的国际会议的旅费，讨论现代代数的核心领域之一（群论）。会议将汇集领先的专家和杰出的年轻研究人员，为报告和讨论该领域令人兴奋的最新进展提供机会。预计将有大约80名数学家参加这次会议。会议将通过帮助确定有趣和具有挑战性的开放问题和新的应用，在该主题的进一步发展中发挥重要作用。地点和时间的选择与上周将在英国华威大学举行的“有限简单群及其应用”独立会议相一致。会议的主题与有限单群的研究有关，这是代数的一个经典领域，两个世纪以来一直是群论研究的核心。单群是所有有限群的基本组成部分，有限单群的分类（CFSG）被广泛认为是20世纪最伟大的数学成就之一，涉及许多研究者多年的研究。这个基本定理在群论和其他领域引发了许多有趣的新问题，并开发了强大的技术来解决这些问题。在cfsg之后的30年左右的时间里，我们对简单群的子群结构和表征理论的理解有了很大的进步。这些主题本身就具有根本的重要性，它们对许多应用程序都是必不可少的。会议将集中讨论简单群的理论，特别强调它们的子群结构和表示。有限和代数单群之间的相互作用将是一个共同的主题，我们将重点关注在群论和其他数学领域的应用，如计算代数、李论、代数几何、数论和模型论。欲了解更多信息，请参阅会议网站https://www.dpmms.cam.ac.uk/~dis20/liebecksaxl/Liebeck-Saxl_2015/Welcome.html

The conference "Simple Groups, Representations, and Related Topics," will be held July 13-15, 2015 at the Center for Mathematical Sciences, University of Cambridge, UK. This grant partially supports travel expenses for US-based researchers, particularly early career mathematicians, to attend this major international conference addressing one of the core areas of modern algebra (group theory). The conference will bring together leading experts and outstanding young researchers, providing an opportunity to report on and discuss exciting recent advances in the field. It is expected that approximately 80 mathematicians will attend the conference. The meeting will play an important role in the further development of the subject by helping to identify interesting and challenging open problems and new applications. The location and timing has been chosen to be compatible with an independent conference on "Finite Simple Groups and their Applications" to be held the previous week at the University of Warwick, UK.The subject of the conference is related to the study of finite simple groups, which is a classical area of algebra that has been at the heart of research in group theory for two centuries. Simple groups are the basic building blocks of all finite groups, and the classification of finite simple groups (CFSG) is widely regarded as one of the greatest mathematical achievements of the 20th century, involving many researchers over a period of many years. This fundamental theorem has led to many interesting new problems in group theory and beyond, and the development of powerful techniques to solve them. In the last thirty years or so, post-CFSG, there have been great advances in our understanding of the subgroup structure and representation theory of simple groups. These topics are of fundamental importance in their own right, and they are essential for many applications. The meeting will focus on the theory of simple groups, with a particular emphasis on their subgroup structure and representations. The interplay between finite and algebraic simple groups will be a common theme, and we will focus on applications, both in group theory and in other areas of mathematics such as computational algebra, Lie theory, algebraic geometry, number theory, and model theory. For more information see the conference web site https://www.dpmms.cam.ac.uk/~dis20/liebecksaxl/Liebeck-Saxl_2015/Welcome.html