Workshop in Equivariant, Chromatic, and Motivic Homotopy Theory

等变、半音和基元同伦理论研讨会

• 批准号: 1261225
• 负责人: Paul Goerss
• 金额: $ 3.4万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1261225&HistoricalAwards=false
• 关键词: Workshop; Equivariant; Chromatic; Motivic; Homotopy

This is a grant for participant support at the "Workshop on Equivariant, Chromatic, and Motivic Homotopy Theory" to be held at Northwestern University from Monday, March 25 to Friday, March 29, 2013. A remarkable number of the main results in homotopy theory of the past few years have been achieved by calculation, following on and benefiting from a period of building and implementing large theory, especially in derived algebraic geometry. The conference organizers hope to emphasize this point, highlighting the recent calculations and explaining what we have learned about basic homotopy theory. The largest success has been the solution of the Kervaire invariant problem and the attendant resurgence in interest in computational techniques in equivariant stable homotopy theory. Complementing this has been more progress in chromatic homotopy theory, both with large spectra, such as ring spectra coming from the theory of topological automorphic forms, and with small spectra, such as the K(2)-local sphere. There have also been new applications of old techniques, as the use of the Goodwillie calculus to study the EHP sequence and the use of Hochschild homology to make difficult calculations in algebraic K-theory.Partly due to the shock provided by the solution of the Kervaire Invariant Problem, a great many young researchers have entered the field of algebraic topology, ranging from beginning graduate students to junior tenure-line faculty. This grant will be used entirely to support the participation of the members of this cohort in the conference. For those with established or emerging research programs the conference will provide a forum to publicize their work; for more junior researchers, the grant will support their attendance and work to integrate them into the wider community.Further information can be found at the Workshop's websitehttp://www.math.northwestern.edu/~pgoerss/newemphasis/

这是一笔资助，用于支持将于2013年3月25日星期一至3月29日星期五在西北大学举行的“等变、色和动同伦理论研讨会”的参与者。在过去的几年中，同伦理论的许多主要结果都是通过计算获得的，这是继并受益于一段时间的大型理论的建立和实施，特别是在推导代数几何中。会议组织者希望强调这一点，强调最近的计算，并解释我们对基本同伦理论的了解。最大的成功是Kervaire不变量问题的解决，以及随之而来的对等变稳定同伦理论计算技术的兴趣的复兴。与此相辅相成的是，在色同伦理论中取得了更大的进展，既有大谱，如来自拓扑自同构形式理论的环谱，也有小谱，如K(2)局域球。旧技术也有新的应用，如使用Goodwillie演算来研究EHP序列和使用Hochschild同调来解决代数k理论中的困难计算。部分由于Kervaire不变量问题的解决所带来的冲击，许多年轻的研究人员进入了代数拓扑领域，从初级研究生到初级终身教职教师。这笔赠款将全部用于支持这批成员参加会议。对于那些已经建立或正在发展的研究项目，会议将提供一个论坛来宣传他们的工作；对于更多的初级研究人员，这笔赠款将支持他们出席会议，并帮助他们融入更广泛的社区。更多的信息可以在研讨会的网站上找到：https://www.math.northwestern.edu/~pgoerss/newemphasis/