Workshop in Equivariant, Chromatic, and Motivic Homotopy Theory

这是对2013年3月25日(星期一)至3月29日(星期五)在西北大学举办的“等变、色和基元同伦理论研讨会”参与者的支持。在过去的几年里，同伦理论的许多主要成果都是通过计算取得的，继承和受益于一段时期的大型理论的建立和实施，特别是在导出的代数几何方面。会议组织者希望强调这一点，突出最近的计算，并解释我们对基本同伦理论的了解。最大的成功是解决了Kervaire不变量问题，并随之而来的是对等变稳定同伦理论中的计算技术的兴趣的复苏。与此相补充的是色同伦理论的更多进展，既有大的谱，如来自拓扑自同构形理论的环谱，也有小的谱，如K(2)-局部球。旧技术也有了新的应用，如使用Goodwillie演算来研究EHP序列，使用Hochschild同调来进行代数K-理论中的困难计算。部分由于Kervaire不变问题的解所带来的冲击，从初级研究生到初级终身教职教师，许多年轻的研究人员进入了代数拓扑学的领域。这笔赠款将完全用于支持这一群体的成员参加会议。对于那些已经建立或正在开展研究计划的人，会议将提供一个论坛来宣传他们的工作；对于更初级的研究人员，这笔拨款将支持他们参加并努力使他们融入更广泛的社区。有关更多信息，请访问研讨会的websitehttp://www.math.northwestern.edu/~pgoerss/newemphasis/

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/