West Coast Algebraic Topology Summer School

该奖项将资助西海岸代数拓扑暑期学校，这是2013年至2016年夏季的一系列课程，旨在帮助在代数拓扑及相关领域工作的早期职业数学家。 这些方案将积极吸引参与者，并在较大和较小的规模之间交替。 在为期一周的大型项目中，针对50至100名参与者，一个大型组委会将计划一些参与者将准备的讲座，然后提出。 一周只有大约15场讲座，留给参与者的时间是解决组委会制定的问题，互相提问（特别是主持人）和组织者，阅读辅助材料，检查自己的笔记，非正式地谈论他们与计划有关的工作，规模较小的三天课程将主要由提供实物和额外财政支持的机构的研究生组织，这些机构包括斯坦福大学、俄勒冈州大学、华盛顿大学和不列颠哥伦比亚省大学。 2013年9月6日至8日，在俄勒冈州大学，该计划将讨论无限类别，这一主题最近已成为代数拓扑及其在代数几何和几何拓扑中应用的一些最重要的近期突破的关键技术。 随着伯克利数学科学研究所即将开展的为期一年的课程，学生组织者选择了解近年来在该学科中开发的最重要的新机器。 在2014年7月，为期一周的计划在不列颠哥伦比亚省的大学（从太平洋研究所的数学科学显着额外的财政和实物支持），该计划将在拓扑场理论。 这些理论的发展需要数学和物理界之间的相互作用，以及代数拓扑学家，几何拓扑学家，微分几何学家和代表理论家之间的数学。 一个旨在解决该理论的不同方面，同时保持连贯性的程序将有助于一代研究人员与一个非常富有成效的子领域进行交互。 2015年和2016年的主题将继续根据其重要性和及时性以及与其他领域的联系进行选择。 2016年的计划可能会集中在色同伦理论，而确定2015年计划的主题将涉及参与者。在所有这些项目中，我们将有更多的专业学习机会，满足早期职业数学家作为教师发展的需求，并为自己的职业发展定位。拓扑学知识对于研究早期宇宙的结构，设计具有最少数量控制器的机器人手臂以及新型数据分析至关重要。 作为形状的基础研究，代数拓扑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）。 西海岸代数拓扑暑期学校选择的主题与这样的连接铭记。 早期职业数学家非常需要研究水平的专业学习，这可以开辟新的研究途径，并扩大他们的专业网络，这可以开辟新的合作。 如果没有这样的早期职业机会，研究项目可能会缩小或完全停滞。 这些需求对于美国西半部的早期职业数学家来说可能更加突出，西半部在地理上比其他地区更加孤立，并且对于来自代表性不足的群体的数学家来说，他们被积极招募成为参与者。 这些暑期学校建立在一系列成功的课程基础上，这些课程在学习深度和培养的专业关系强度方面都超出了预期。 许多参与者报告说，这些经历是变革性的，我们希望这些经历在2013-2016年的系列中继续下去。 这些经验的积极学习方面不仅告知参与者的研究计划，但他们的教学方法以及。 因此，该计划的影响超越了数学和科学研究，以中学后，甚至K-12教育。

This award will fund the West Coast Algebraic Topology Summer School, a series of programs in the summers from 2013-2016 aimed at early-career mathematicians who work in algebraic topology and related areas. The programs will actively engage the participants, and alternate between larger and smaller scale. In the larger week-long programs, aiming for between 50 and 100 participants, a large organizing committee will plan lectures which some participants will prepare and then present. There will only be about 15 lectures for the week, leaving time for participants to work on problems formulated by the organizing committee, to ask questions of each other (especially the presenters) and the organizers, to read supporting materials and go over their own notes, to talk informally with each other about their work related to the program, etc. The smaller three-day programs will be primarily organized by graduate students from institutions providing both in-kind and additional financial support, namely Stanford University, the University of Oregon, the University of Washington, and the University of British Columbia. In September 6-8, 2013 at the University of Oregon the program will be on Infinity Categories, a topic which has recently become a key technical piece of some of the most significant recent breakthroughs in algebraic topology and its applications to algebraic geometry and geometric topology. With the upcoming yearlong program at the Mathematical Sciences Research Institute in Berkeley, the student organizers have chosen to learn about arguably the most important new machinery developed in the subject in recent years. In July 2014, the week-long program at the University of British Columbia (with significant additional financial and in-kind support from the Pacific Institute for the Mathematical Sciences), the program will be on Topological Field Theories. Development of these theories requires interplay both between the mathematics and physics communities, and within mathematics between algebraic topologists, geometric topologists, differential geometers, and representation theorists among others. A program designed to address the different aspects of the theory while being coherent will aid a generation of researchers in interfacing with a remarkably fruitful subfield. The topics in 2015 and 2016 will continue to be chosen based on their importance and timeliness and connections with other fields. The 2016 program will likely focus on Chromatic Homotopy Theory, while determining the topic for the 2015 program will involve the participants. At all of these programs, we will have additional opportunities for professional learning addressing needs for early-career mathematicians to develop as teachers and to position themselves for career growth.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 new kinds of data analysis. In its role as a basic study of shape, algebraic 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). The West Coast Algebraic Topology Summer School chooses topics with such connections in mind. Early career mathematicians have a great need for research-level professional learning, which can open up new research pathways, and for enlarging their professional networks, which can open up new collaborations. Without such early-career opportunities, research programs can narrow or stall out altogether. These needs can be more prominent for early career mathematicians in the western half of the United States, which is more geographically isolated than other regions, and for mathematicians from under-represented groups, who are actively recruited to be participants. These summer schools build on a series of successful programs which have exceeded expectations in both the depth of learning and the strength of professional relationships fostered. Many participants have reported them to be transformative experiences, and we expect those kinds of experiences to continue in our series from 2013-2016. The active learning aspects of these experiences inform not only the research programs of participants but their approach to pedagogy as well. Thus the program's impact goes beyond mathematical and scientific research to postsecondary and even K-12 education.