李谷川博士，北京大学

Chromatic homotopy theory uses the algebraic geometry of smooth 1-parameter formal groups to separate stable homotopy theory into periodic layers. The 1st layer recovers the image of Adams’ J homomorphism and the real Bott periodicity of the real topological K-theory KO. In this talk, I will present how the equivariant techniques lead to generalizations of these results to general layers at the prime 2. The proof takes inspiration from the breakthroughs of Hill-Hopkins-Ravenel’s solution to Kervaire invariant one problem. This talk is based on past and current works with Zhipeng Duan, XiaoLin Danny Shi, Guozhen Wang, Zhouli Xu, and Ningchuan Zhang.