Abstract: In filtration 1 of the Adams spectral sequence, using secondary cohomology operations, Adams computed the differentials on the classes h_j, resolving the Hopf invariant one problem. In Adams filtration 2, using equivariant and chromatic homotopy theory, Hill--Hopkins--Ravenel proved that the classes h_j^2 support non-trivial differentials for j \geq 7, resolving the celebrated Kervaire invariant one problem. 

I will talk about joint work with Robert Burklund: In Adams filtration 3, we prove an infinite family of non-trivial d_4-differentials on the classes h_j^3 for j \geq 6, confirming a conjecture of Mahowald. Our proof uses two different deformations of stable homotopy theory – C-motivic stable homotopy theory and F_2-synthetic homotopy theory – both in an essential way.

报告人简介：徐宙利，2008年本科毕业于北京大学，2017年获得芝加哥大学博士学位，目前是加州大学圣迭戈分校数学系副教授。徐宙利的研究方向是代数拓扑，主要从事球面同伦群的研究，与合作者在球面稳定同伦群的计算上取得了重大突破，受邀在2022年国际数学家大会上做分会报告。