温州大学数理学院2025年第20期数理大讲堂

报告题目：The generalized Tate diagrams of the equivariant slice filtration

报告人：闫国旗 博士

主持人：沈文

报告时间：2025年11月18日上午10：00-11：00

报告地点：3B205。

摘要 ：The equivariant slice spectral sequence is invented by Dugger and is generalized and utilized to a great extent by Hill-Hopkins-Ravenel in their resolution of the Kervaire invariant one problem. Later, because of the work of Hahn-Shi and Meier-Hill-Shi-Zeng, the equivariant slice spectral sequence can be used to compute the homotopy fixed point of Lubin-Tate theories.

In this talk, I will talk about equivariant computations around the slice spectral sequence using the generalized Tate diagrams invented by Greenlees-May. I will first talk about my own work on computations of the E_2-pages of the slice spectral sequence and its localized variants. Then I will talk about my joint work with Yutao Liu and XiaoLin Danny Shi on exploring the effect of applying the generalized Tate diagrams on the slice filtration. We extend the transchromatic phenomenon and vanishing lines proved by Meier-Shi-Zeng for connective HHR theories to the periodic versions. Using the Tate spectral sequence, we illustrate the duality of differentials in the slice spectral sequence. This enables us to go back and forth between differentials in the positive and negative cones.

报告人简介：

闫国旗本科毕业于北京理工大学，硕士毕业于南开大学，博士毕业于美国圣母大学，现为复旦大学上海数学中心博士后。研究方向为代数拓扑，等变同伦论等。在Algebr. Geom. Topol.，Proc. Amer. Math. Soc.等知名国际数学期刊发表多篇论文。其博士导师Mark Behrens是著名代数拓扑学家，国际代数拓扑领军人物。