中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

华罗庚青年数学论坛

学术报告

报告人: 孔嘉  博士(Institute for Advanced Study, Princeton, USA
  目:The motivic Chow t-structure
  间:2022.05.16(星期一),10:00-12:00
  点:腾讯会议:593-874-852
  要:Work of Gheorghe--Wang--Xu defined the Chow-Novikov t-structure on a p-completed cellular motivic module category. One application of this t-structure is in classical Adams spectral sequence computation by Isaksen--Wang--Xu. I will first talk about this t-structure and relevant results that lead to the computation applications. Then I will introduce another t-structure, the Chow t-structure on the motivic stable homotopy category over a general base field. This is defined in the joint work with Tom Bachmann, Guozhen Wang and Zhouli Xu. The Chow t-structure is a generalization of the Chow-Novikov t-structure. We identify the heart of this t-structure, and expand the results of Gheorghe-Wang-Xu to integral results on the entire motivic category over general base fields. The generalization also leads to computational applications on determining the Adams spectral sequences in the classical stable homotopy category, as well as that in the motivic stable homotopy category over C, R, and F_p. 

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报告人: 孔嘉  博士Institute for Advanced Study, Princeton, USA
  目:Motivic slice spectral sequences and an equivariant application
  间:2022.05.19(星期四),10:00-12:00
  点:腾讯会议:932-907-736
  要:Slice spectral sequences are important calculation tools in motivic stable homotopy theory. I will talk about the definitions and examples. In particular, in work with Eva Belmont and Dan Isaksen, we calculate the homotopy of the R-motivic image-of-j spectrum using effective slice spectral sequence. For the second part of this talk, I will talk about how the motivic effective slice spectral sequence leads to a new C_2-equivariant spectral sequence. It turns out this new spectral sequence is supprisingly efficient in calculating the equivariant connective real K theory spectrum.

 

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