New directions in the model theory of fields: an LMS Durham research symposium

模型论是数理逻辑的一个分支，从一阶逻辑可定义性的角度处理数学结构(模型)。传统上，这门学科被细分为两个高度重叠的领域：纯模型理论和应用模型理论。后者的特点是它对代数、几何和分析的应用和影响。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，由D.Macpherson(利兹)、A.Pillay(利兹)、M.Prest(曼彻斯特)和A.Wilkie(曼彻斯特)组织。本课程将集中于应用模型理论及其在主流数学的某些特定领域的应用。我们将邀请来自世界各地的许多主流数学家，他们已经接受或表示有兴趣熟悉模型理论方法。会议结束后，模型理论家们将更好地了解研讨会涵盖的主流数学领域中适合他们的方法的问题，从而更好地解决这些问题。此外，在场的数学家将更多地意识到模型理论方法在他们自己的学科中的范围。会议将集中讨论显示出特殊前景的主题，以及不同群体之间的互动可能最有益的主题。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所面临的技术和挑战。为了帮助实现这一目标，我们将就这三个主题分别进行一系列简短的讲座。每个系列将有两场来自模型理论家的讲座和两场来自非模型理论家的讲座。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。会议结束后一个月内，将通过网络摄像头(经发言者允许)对主要会议进行录音，并在网站上免费提供。课堂讲稿和/或幻灯片也将放在网站上。更详细的会议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领域和相关领域的模型理论研究产生重大而持久的推动作用。

Model theory is a branch of mathematical logic dealing with mathematical structures (models) from the point of view of first-order logical definability. Traditionally the subject has been subdivided into two, highly overlapping, areas: pure model theory and applied model theory. The latter is characterized by its applications to, and influences from, algebra, geometry and analysis.We propose to hold a 10-day conference in July 2009 at Durham University, organised by D. Macpherson (Leeds), A. Pillay (Leeds), M. Prest (Manchester) and A. Wilkie (Manchester). This will concentrate on applied model theory and its applications to certain specific areas of mainstream mathematics. We will invite many mainstream mathematicians from around the world who have taken on board, or expressed an interest in familiarizing themselves with, model theoretic methods. After the meeting, the model theorists will have a better understanding of those problems in the areas of mainstream mathematics covered in the symposium that are amenable to their methods, and therefore be in a better position to solve them. Also, the mathematicians present will become more aware of the scope of model theoretic methods within their own disciplines. The conference will focus on themes which show particular promise, and where interactions between different groups are likely to be of most benefit. There will be an uncluttered lecture programme, with ample opportunities for discussions, collaborations and informal talks. Our aim is to ensure that all are aware of the techniques and challenges that are arising for our areas of focus. To help achieve this we will have a short series of lectures on each of the three themes. Each series will have two lectures from a model theorist and two from a non-model theorist. 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) via a web-cam, and be made freely available on the website within one month of the finish of the meeting. Lecture notes and/or slides will also be put on the site. 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 the model theory of fields and related areas.