SM: West Coast Algebraic Topology Summer School

SM：西海岸代数拓扑暑期学校

• 批准号: 0963813
• 负责人: Dev Sinha
• 金额: $ 3万
• 依托单位: University of Oregon Eugene
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0963813&HistoricalAwards=false
• 关键词: SM; West; Coast; Algebraic; Topology

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.

PI，拉尔夫科恩和德夫辛哈，将是一个为期一周的代数拓扑学暑期学校课程的计划组织者，将于2010年夏天在俄勒冈州大学举办。这个暑期学校将侧重于代数拓扑和代数几何之间的接口，特别是模空间。我们将把30名研究生和早期职业数学家聚集在一起，介绍一个已经成熟的领域，其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，学生将学习映射类组，稳定性定理，运算操作和其他loopspace机械，配边光谱，奇点理论，配边类别和拓扑场论。计算将在相关时予以强调。这个暑期学校将使用一种独特的教学工具，结合在其他环境中取得成功的元素。年轻的研究人员将参与组织和演讲。参加者将被鼓励工作的问题，填写背景，并做阅读一起除了参加讲座。西海岸拓扑学暑期学校将尽全力招募广泛而多样化的参与者，将显著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（组合数学）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，拓扑学的知识是必不可少的，例如在研究早期宇宙的结构，在设计一个机器人手臂与最小数量的控制器，并在搜索大数据集的有意义的分组，最近成功地做了乳腺癌的研究。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本领域之间的联系。来自代表性不足背景的数学家将被大力招募。研究生和博士后将获得与当代数学的一些最重要的发展实践经验，准备他们成为该领域的未来领导者。 与会者将扩大他们的专业网络，这是特别重要的考虑到地理距离所面临的数学家在北美西半部。组织者和参与者还将有机会反思所使用的一系列教学工具，并可能在培训研究生和本科生或与科学家同行和公众接触时使用一些工具。