Seminar by Guchuan Li: Real Bott periodicity at higher chromatic heights
Date: Monday, April 21
Venue: Room 204, Hai Na Yuan #2 海纳苑2幢204室
Speaker: Guchuan Li 李谷川 (Peking University 北京大学）
Pretalk: Bott Periodicity and topological K-theory
Time: 16:15-16:45
Abstract: We will assume Bott Periodicity and use it to define a generalized cohomology theory: topological K-theory.
Research talk: Real Bott periodicity at higher chromatic heights
Time: 16:45-17:35
Abstract: Real Bott periodicity shows that the homotopy groups of real topological K-theory is 8-periodic. From chromatic homotopy theory perspective, Real topological K-theory is a height 1 theory, and for each natural number n, there are height n periodic cohomology theories. Important examples include 192 periodic topological modular forms at height 2 and Hill-Hopkins-Ravenel’s 256 periodic Kervarie detection spectrum at height 4. In this talk, we give a general formula for the periodicity for all heights. This is joint work with Zhipeng Duan, Mike Hill, Yutao Liu, Danny XiaoLin Shi, Guozhen Wang, and Zhouli Xu.
