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.

该奖项资助美国的初级研究数学家前往参加在英国剑桥艾萨克·牛顿数学科学研究所举办的四个讲习班。这些研讨会，同伦利用更高的结构学期计划的所有部分是“同伦理论中的更高结构”（2018年7月2日至6日），“等变和动机同伦理论”（2018年8月13日至17日），“导出代数几何和色同伦理论”（2018年9月24日至28日）和“流形”（2018年12月3日至7日）。在过去的15年里，出现了文艺复兴的代数拓扑。 老问题用新方法解决，新方法引出新思想，新思想引出新问题，新问题引出新定理。在每一种情况下，在引入和研究更高的结构之后都有巨大的进步。在牛顿研究所的更大的计划将评估已经做了什么，突出什么是行之有效的，发展领域，给教学和研究研讨会，并提供一个会议场所，为研究人员在该领域的各个分支的各级。将有驻场数学家，但更大的社区将通过四个研讨会纳入其中。该奖项将仅用于支持美国研究生、博士后研究员和初级教师参与研讨会，无需其他重大支持。NSF资助的直接影响将是多达30名初级研究人员的培训和职业发展，他们将有机会参加牛顿研究所的一个重大项目，该研究所是数学领域的一个重要国际联系点。第二个影响是进一步发展新兴的研究小组之间的合作，在代数拓扑和派生代数几何在美国和欧洲。四个工作坊各有不同的侧重点和风味。第一，在更高的结构，是集中在基础和基础的应用，并明确针对新的研究人员到该领域。第二，在等变和动机同伦理论，将是一个重要的研究会议上的一个重要和非常活跃的领域。第三，派生代数几何和色同伦理论，是一个新兴的主题和经典领域的融合;年轻的研究人员在这个新的领域的混合物一直很重要。最后，流形的代数拓扑已经成为同伦理论，导出几何和数学物理的知识十字路口;这个研讨会的目的是作为跨学科的对话，庆祝丰富的发展。所有这些讲习班的明确目标是，不仅要吸收新的声音作为听众参与者，而且还要吸收新的声音作为发言者。研讨会的网站可以在www.example.com上找到https://www.newton.ac.uk/event/hhh/workshopsThis奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。