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

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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 .