BIMSA > BIMSA TQFT and Higher Symmetries Seminar BIMSA TQFT and Higher Symmetries Seminar The hastened Adams spectral sequence for supercohomology
The hastened Adams spectral sequence for supercohomology
Organizers
Ansi Bai , Hank Chen , Liang Kong , Yilong Wang , Zhihao Zhang , Hao Zheng
Speaker
Arun Debray
Time
Tuesday, March 24, 2026 9:45 AM - 11:45 AM
Venue
A3-3-301
Online
Zoom 537 192 5549 (BIMSA)
Abstract
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.