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.

该奖项资助来自美国的初级研究数学家参加将在英国剑桥艾萨克·牛顿数学科学研究所举办的四个研讨会的旅费。这些工作坊都是关于同伦利用更高结构的学期课程的一部分，分别是“同伦理论中的更高结构”(2018年7月2日至6日)、“等变与动机同伦理论”(2018年8月13日至17日)、“派生代数几何与色同伦理论”(2018年9月24日至28日)和“流形”(2018年12月3日至7日)。过去的十五年见证了代数拓扑学的复兴。老问题用新方法解决，新方法产生新思想，新思想产生新问题，新问题产生新定理。在每一种情况下，在引入和研究高级结构之后都有了巨大的进步。牛顿研究所的这个更大的项目将评估已经完成的工作，突出哪些工作做得很好，开发该领域，举办教学和研究研讨会，并为该领域各个分支的所有级别的研究人员提供一个聚会场所。将有数学家入驻，但更大的社区将通过四个工作坊纳入。该奖项将仅用于支持美国研究生、博士后研究员和初级教员参加研讨会，而不提供其他重要支持。NSF资助的直接影响将是最多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主要项目，该研究所是数学领域的一个主要国际联系机构。第二个影响是进一步发展美国和欧洲在代数拓扑学和派生代数几何领域的新兴研究小组之间的合作。四个工作坊各有不同的侧重点和风格。第一，关于更高的结构，重点是基础和基础的应用，明确针对该领域的新手研究人员。第二次是关于等变和理据同伦理论的，这将是该领域一个重要和非常活跃的领域的重要研究会议。第三，关于派生代数几何和色同伦理论，是一个新兴主题和一个经典领域的混合；年轻的研究人员在这个新的混合领域中发挥了重要作用。最后，流形的代数拓扑已经成为同伦理论、衍生几何和数学物理的智力十字路口；这个研讨会旨在成为庆祝大量发展的跨学科对话。所有这些讲习班的明确目标是吸收新的声音，不仅作为听众参与者，而且还作为演讲者。研讨会的网站可以在https://www.newton.ac.uk/event/hhh/workshopsThis网站上找到，该奖项反映了国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。