SM: West Coast Algebraic Topology Summer School

两位pi， Ralph Cohen和Dev Sinha，将是一个为期一周的代数拓扑暑期学校项目的组织者，该项目将于2010年夏天在俄勒冈大学举办。本暑期课程将着重于代数拓扑和代数几何之间的界面，特别是模空间。我们将邀请30名研究生和早期职业数学家一起介绍一个已经成熟的研究领域，他们的技术将为整个拓扑学的发展提供信息和启发。在其他主题中，学生将学习映射类群、稳定性定理、操作动作和其他环空间机制、协协谱、奇点理论、协协范畴和拓扑场理论。只要计算是相关的，就会强调。这个暑期学校将使用独特的教学工具，结合在其他环境中成功的元素。年轻的研究人员将参与组织和发表演讲。除了参加讲座外，参加者还将被鼓励解决问题，填写背景资料，一起阅读。将作出充分努力，招募广泛和多样化的参与者。西海岸拓扑学暑期学校将大大加强拓扑学家和其他使用拓扑学的人的知识基础。作为形状的基础研究，拓扑学在数学的其他领域有着重要的分支，从基本的计数问题（组合学）到方程的解（代数），再到微积分的应用和扩展（分析）。更广泛地说，拓扑知识是必不可少的，例如，在研究早期宇宙的结构，设计具有最少数量控制器的机械臂，以及在寻找有意义的分组的大型数据集（最近成功地用于研究乳腺癌）中。暑期学校的结构将突出几何和代数的分支，从而加强理论数学基础领域之间的联系。将大力招募来自代表性不足背景的数学家。研究生和博士后将获得一些当代数学最重要发展的实践经验，为他们成为该领域未来的领导者做好准备。参与者将扩大他们的专业网络，考虑到北美西半部数学家所面临的地理距离，这一点尤为重要。组织者和参与者也将有机会反思所采用的一系列教学工具，并可能在培训研究生和本科生或与其他科学家和公众接触时使用其中一些工具。

The PIs, Ralph Cohen and Dev Sinha, will be program organizers for a one-week summer school program in algebraic topology, to be hosted at the University of Oregon in the summer of 2010. This summer school will focus on the interface between algebraic topology and algebraic geometry, in particular on moduli spaces. We will bring thirty graduate students and early-career mathematicians together for an introduction to an area which is ripe for investigation, and whose techniques will inform and inspire developments throughout topology. Among other topics, students will learn about mapping class groups, stability theorems, operad actions and other loopspace machinery, cobordism spectra, singularity theory, cobordism categories, and topological field theories. Calculations will be emphasized whenever they are relevant. This summer school will use a unique blend of pedagogical tools, combining elements which have been successful in other settings. Younger researchers will be involved with both organizing and giving talks. Attendees will be encouraged to work problems, fill in background, and do reading together in addition to attending lectures. A full effort will be made to recruit a broad and diverse group of participants.The west coast topology summer school will significantly strengthen the knowledge base of topologists and others who use topology. In its role as a basic study of shape, topology has significant ramifications in other areas of mathematics, from basic counting problems (combinatorics) to solutions of equations (algebra) to applications and extensions of the calculus (analysis). More broadly, knowledge of topology is essential for example in studying the structure of the early universe, in designing a robot arm with a minimal number of controllers, and in searching large data sets for meaningful groupings as successfully done recently for study of breast cancer. The summer school will be structured to highlight ramifications in geometry and algebra, and thus strengthen the ties between basic areas of theoretical mathematics. Mathematicians from underrepresented backgrounds will be vigorously recruited. Graduate students and post-docs will gain hands-on experience with some of the most important developments of contemporary mathematics, preparing them to be future leaders of the field. Participants will enlarge their professional networks, which is especially critical given the geographical distances faced by mathematicians in the western half of North America. Organizers and participants will also have the opportunity to reflect upon the array of pedagogical tools employed, and might employ some themselves in training graduate students and undergraduates or reaching out to fellow scientists and the general public.