Time：10:00-11:00, Friday, June 10th, 2022
ZOOM ID：884 1427 1305
Passcode：458251
Host:Dr. Xing Gu, Institute for Theoretical Sciences, Westlake University
Speaker:Dr. Guchuan Li, University of Michigan
Title:Vanishing results in Chromatic homotopy theory at prime 2
Biography：
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.
Abstract:
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.
