Smooth structures, stable homotopy groups of spheres and motivic homotopy theory

讲座时间 Datetime: 

星期五, 2018/01/12 - 从 14:30 到 16:00

地点 Venue: 

海滨红楼6号楼1楼会议室

报告人 Speaker: 

徐宙利 博士

单位 Affiliation: 

Massachusetts Institute of Technology

报告摘要 Abstract: 

Following Kervaire-Milnor, Browder and Hill-Hopkins-Ravenel, Guozhen Wang and I showed that the 61-sphere has a unique smooth structure and is the last odd dimensional case: $S^1, S^3, S^5$ and $S^{61}$ are the only odd dimensional spheres with a unique smooth structure. The proof is a computation of stable homotopy groups of spheres. We introduce a method that computes differentials in the Adams spectral sequence by comparing with differentials in the Atiyah-Hirzebruch spectral sequence for real projective spectra through Kahn-Priddy theorem. I will also discuss recent progress of computing stable stems using motivic homotopy theory with Dan Isaksen and Guozhen Wang.