Combinatorial and Geometric Structures in Representation Theory: An LMS Durham Research Symposium

在诞生100多年后，表示论是一个充满活力、不断发展的数学研究领域。这是一个非常广泛的话题，跨越了许多领域，它提供了一种在许多其他数学领域都很有价值的思维方式。我们建议于2009年7月在达勒姆大学举办一个为期10天的会议，题为《表示理论中的组合和几何结构》，由J.Brundan(俄勒冈州)、J.Chuang(伦敦金融城)、I.Gordon(爱丁堡)和B.Leclerc(Caen)组织。这将是LMS达勒姆研讨会系列中的一部分，并将集中在表示理论的组合、代数和几何方面的最新发展。我们将把这些领域的顶尖英国和国际研究人员聚集在一起，在达勒姆LMS研讨会提供的非正式气氛中，目的是找到共同点并讨论令人兴奋的最新发展。这将为交流思想和交流研究专业知识提供机会，我们相信，如果这项提议取得成果，将实现令人兴奋的新的国际合作。我们还将邀请有前途的年轻英国研究人员，让他们有机会向国际专家学习和互动，特别是与他们讨论他们的工作。研讨会将有一个整洁的讲座计划，有大量的讨论、合作和非正式会谈的机会。我们的目标是确保所有人都意识到我们的重点领域正在出现的新技术和新挑战。通过汇聚广泛的专家，这次会议将对这些丰富的研究领域的发展产生重大影响。会议结果最初将通过一个积极管理和易于访问的网站分发，该网站将载有与会者名单、谈话摘要和其他相关信息。主要会谈将用摄像机录制(经发言者允许)，并将在会议结束后一个月内放在网站上。讲座讲稿和/或幻灯片也将放在网站上，所有这些材料都将免费提供给所有人。会议的更详细记录将通过在研究期刊上发表受会议主题启发的前沿文章来提供。预计这次会议将对世界上几个相关领域的表征理论的研究产生重大而持久的推动作用。

More than 100 years after its birth, representation theory is a vibrant, growing research area of mathematics. It is a very broad topic which crosses many fields, and it provides a way of thinking that has been valuable in many very other mathematical areas. We propose to hold a 10-day conference in July 2009 at Durham University, entitled ``Combinatorial and Geometric Structures in Representation Theory'', and organised by J. Brundan (Oregon), J. Chuang (City, London), I. Gordon (Edinburgh) and B. Leclerc (Caen). This will be in the series of LMS Durham Symposia, and will concentrate on recent developments in combinatorial, algebraic and geometric aspects of representation theory. We will bring together the top UK and international researchers in these fields in the informal atmosphere provided by an LMS Durham Symposium, with the aim of finding common ground and discussing exciting recent developments. This will give the opportunity for the exchange of ideas and cross-fertilization of research expertise, and we are confident that exciting new international collaborations will be realised if this proposal comes to fruition. We will also invite promising young UK researchers, and give them the opportunity to learn from and interact with the international experts and, in particular, to discuss their work with them.The symposium will have an uncluttered lecture programme, with ample opportunities for discussions, collaborations and informal talks. Our aim is to ensure that all are aware of new techniques and the new challenges that are arising for our areas of focus. By bringing together a broad range of experts, this meeting will have a significant impact on the development of these rich areas of research. The results of the meeting will be distributed initially via an actively-managed and easily accessible website, which will contain a list of participants, abstracts of talks and other relevant information. The main talks will be recorded (with permission of the speakers) with a camcorder, and will be placed on the website within one month of the finish of the meeting. Lecture notes and/or slides will also be put on the site, and all this material will be made freely available to all.A more detailed record of the meeting will be provided by the publication in research journals of cutting-edge articles inspired by the subjects covered in the meeting. The conference is expected to provide a major lasting fillip to world research in several related areas of representation theory .