Alice Hedenlund: Multiplicative spectral sequences in infinity-land

ABSTRACT:   Spectral sequences have proven immensely powerful tools in modern mathematics. Unfortunately, they have gathered a, not completely unfounded, reputation of being “difficult” and “complicated”. This goal of this talk is act as an introduction to the construction of spectral sequences, as well as providing a new perspective for people who are already familiar with the topic, via the language of stable infinity categories. The focus lies on clarifying what is needed to put a multiplicative structure on spectral sequences. We will specifically look at the case of the Tate spectral sequence, a spectral sequence where multiplicativity is quite hard to pin down in the classical setting, but where it is very straight-forward in the infinity-categorical framework. This is all work in progress joint with Achim Krause and Thomas Nikolaus.