Workshops: Homotopy Harnessing Higher Structures

研讨会：利用更高结构的同伦

• 批准号: 1833295
• 负责人: Paul Goerss
• 金额: $ 3万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-07-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1833295&HistoricalAwards=false
• 关键词: Workshops; Homotopy; Harnessing; Higher; Structures

This award supports travel for junior research mathematicians from the United States to participate in four workshops to be held at the Isaac Newton Institute for Mathematical Science in Cambridge, England. These workshops, all part of the semester program on Homotopy Harnessing Higher Structures are "Higher Structures in Homotopy Theory" (July 2-6, 2018), "Equivariant and Motivic Homotopy Theory" (August 13-17, 2018), "Derived Algebraic Geometry and Chromatic Homotopy Theory" (September 24-28, 2018), and "Manifolds" (December 3-7, 2018). The last fifteen years have seen a renaissance for algebraic topology. Old problems have been solved using new methods, new methods led to new ideas, new ideas to new problems, and new problems to new theorems. In each case, there was enormous progress after the introduction and the study of higher structures. The larger program at the Newton Institute will assess what has been done, highlight what is working well, develop the field, give instructional and research workshops, and provide a meeting place for researchers at all levels of the various branches of the field. There will be mathematicians in residence, but the larger community will be incorporated through the four workshops.This award will be used solely to support the workshop participation of US graduate students, postdoctoral fellows, and junior faculty without other significant support. The direct impact of NSF funding will be the raining and career development of up to 30 junior researchers, who will gain the opportunity to participate in a major program at the Newton Institute, which is a major international nexus in mathematics. A secondary impact is to further develop collaboration between emerging research groups in algebraic topology and derived algebraic geometry in the US and Europe. Each of the four workshops has a different emphasis and flavor. The first, on higher structures, is focused on the foundations and applications of foundations, and is expressly aimed at researchers new to the field. The second, on equivariant and motivic homotopy theory, is set to be a major research conference on a vital and extremely active area in the field. The third, on derived algebraic geometry and chromatic homotopy theory, is a blend of an emerging topic and a classical area; younger researchers have been important in this new mixture of fields. Finally, the algebraic topology of manifolds has become an intellectual crossroads for homotopy theory, derived geometry, and mathematical physics; this workshop is intended as cross-disciplinary dialog celebrating a wealth of developments. It is the expressed aim of all of these workshops to incorporate new voices not simply as audience participants, but as speakers as well. The website of the workshops can be found at https://www.newton.ac.uk/event/hhh/workshopsThis award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该奖项支持来自美国的初级研究数学家的旅行，参加了四个在英格兰剑桥的艾萨克·牛顿数学科学研究所举行的研讨会。这些讲习班的所有学期课程的一部分都在同义验证方案较高的结构上是“同义理论中的较高结构”（2018年7月2-6日），“均等和动机同义理论”（2018年8月13日至17日），“代数几何学和色谱和色谱理论”（9月24-28，2018年9月24-28，2018年，和2018年），以及2018年（2018年9月24-28），2018年（2018年）。过去的十五年已经为代数拓扑复兴了。 已经使用新方法解决了旧问题，新的方法导致了新的想法，新问题的新想法以及新定理的新问题。在每种情况下，引入后都有巨大的进步和较高结构的研究。牛顿学院的较大计划将评估所做的工作，突出显示出良好的工作，开发该领域，提供教学和研究研讨会，并为该领域各个分支机构的研究人员提供聚会场所。居住地将有数学家，但较大的社区将通过四个研讨会进行合并。该奖项将仅用于支持美国研究生，博士后研究员和初级教职员工的研讨会参与，而没有其他重大支持。 NSF资金的直接影响将是最多30名初级研究人员的下雨和职业发展，他们将有机会参加牛顿学院的主要计划，牛顿学院是数学领域的主要国际联系。次要影响是进一步发展代数拓扑的新兴研究小组与美国和欧洲的代数几何形状之间的合作。四个研讨会中的每一个都有不同的重点和风味。首先，在更高的结构上，重点是基础的基础和应用，并明确针对该领域的研究人员。第二个关于模棱两可和动机同义理论，将成为有关该领域至关重要且极为活跃的领域的主要研究会议。第三个是关于衍生的代数几何和色谱理论，是新兴主题和经典领域的融合。年轻的研究人员在这种新的领域中很重要。最后，流形的代数拓扑已成为同型理论，衍生几何和数学物理学的智力十字路口。该研讨会的目的是作为跨学科对话框庆祝许多发展。所有这些研讨会的表达目的是将新的声音不仅仅作为观众参与者，而且还融合了演讲者。可以在https://www.newton.ac.uk/event/hhh/workshopsthis奖上找到该研讨会的网站，反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛影响的审查标准来评估的。