时间：2022年6月10日（星期五）10:00-11:00
地点：ZOOM
ZOOM会议号：884 1427 1305
密码：458251
主持人：西湖大学理论科学研究院 古星博士
主讲人：密歇根大学 李谷川博士
报告题目：Vanishing results in Chromatic homotopy theory at prime 2
主讲人简介：
Guchuan Li is a Postdoctoral Assistant Professor at University of Michigan, Ann Arbor. He completed his Ph.D. in 2019 at Northwestern University, under the supervision of Paul Goerss. His research interest is algebraic topology, with a particular emphasis on chromatic and equivariant homotopy theory.
报告摘要:
Chromatic homotopy theory is a powerful tool to study periodic phenomena in the stable homotopy groups of spheres. Under this framework, the homotopy groups of spheres can be built from the fixed points of Lubin--Tate theories $E_h$. These fixed points are computed via homotopy fixed points spectral sequences. In this talk, we prove that at the prime 2, for all heights $h$ and all finite subgroups $G$ of the Morava stabilizer group, the $G$-homotopy fixed point spectral sequence of $E_h$ collapses after the $N(h,G)$-page and admits a horizontal vanishing line of filtration $N(h,G)$.
Our proof uses new equivariant techniques developed by Hill--Hopkins--Ravenel in their solution of the Kervaire invariant one problem. If time allows, Dr Li will present two applications: how this vanishing result significantly simplifies computation like the homotopy groups of topological modular forms at the prime 2, and gives $E_n^{hG}$-orientations of Real vector bundles at the prime 2.
This is joint work with Zhipeng Duan and XiaoLin Danny Shi.
