Simple groups, representations, and related topics

2015年7月13日至15日，将在英国剑桥大学数学科学中心举行“简单小组、陈述和相关话题”会议。这笔赠款部分资助了美国的研究人员，特别是早期职业数学家，参加这个涉及现代代数(群论)核心领域之一的重大国际会议的旅费。会议将汇集领先的专家和杰出的年轻研究人员，提供一个报告和讨论该领域令人兴奋的最新进展的机会。预计将有大约80名数学家参加会议。会议将通过帮助确定有趣和具有挑战性的未决问题和新的应用，在这一主题的进一步发展中发挥重要作用。地点和时间的选择是为了与前一周在英国华威大学举行的关于“有限单群及其应用”的独立会议相兼容。会议的主题与有限单群的研究有关，这是一个经典的代数领域，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构件，而有限单群的分类被广泛认为是20世纪最伟大的数学成就之一，涉及了许多研究者多年的时间。这一基本定理导致了群论内外许多有趣的新问题，以及解决这些问题的强大技术的发展。在过去的三十多年里，在后CFSG时代，我们对单群的子群结构和表示理论的理解有了很大的进步。这些主题本身就具有基本的重要性，并且对于许多应用程序都是必不可少的。会议将集中讨论单群的理论，特别强调其子群的结构和表示。有限单群和代数单群之间的相互作用将是一个共同的主题，我们将专注于在群论和其他数学领域的应用，如计算代数、李理论、代数几何、数论和模型论。欲了解更多信息，请访问会议网站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