-

The hastened Adams spectral sequence for supercohomology

组织者

白岸斯 , 陈群皓 , 孔良 , 王亦龙 , 张智浩 , 郑浩

演讲者

Arun Debray

时间

2026年03月24日 09:45 至 11:45

地点

A3-3-301

线上

Zoom 537 192 5549 (BIMSA)

摘要

The Atiyah-Hirzebruch and Adams spectral sequences have become standard tools in the mathematical physics literature for computing generalized (co)homology groups. Recently, a generalized cohomology theory called "(extended) supercohomology" has appeared as an essential ingredient in the classification of fusion 2-categories, with applications to 4d TFT. However, neither the Atiyah-Hirzebruch nor the Adams spectral sequence is effective at computing supercohomology. In this talk, I will discuss work joint with Weicheng Ye and Matthew Yu applying the hastened Adams spectral sequence (HASS) of Behrens-Hopkins-Hill-Mahowald and Bruner-Rognes to twisted supercohomology. We compute the E2-page and show that running the HASS is tractable in examples. With time permitting, I will discuss two applications: one towards a question of Córdova-Ohmori on symmetry-enforced gaplessness in 4d, and another towards the question of why (or whether) the Adams spectral sequence is more powerful than the Atiyah-Hirzebruch spectral sequence for computing groups of SPTs.