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

综合报告

报告人： 李谷川 博士（北京大学）

题  目：Equivariant techniques in Chromatic homotopy theory

时  间：2023.05.12（星期五），09:00-10:00

地  点：数学院南楼N202

摘  要：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.