Appears in collection : 2023 - T2 - WS1 - GAP XVIII: Homotopy algebras and higher structures

Spectral sequences arise as algebraic tools in many areas of mathematics. Of particular interest are spectral sequences of filtered complexes and multicomplexes. Questions addressed during the talk: how to compare spectral sequences? Can we invert some class of weak equivalences, as e.g. morphisms realizing an isomorphism from a given page and afterwards? This is a long project with S. Whitehouse and I will explain some model category structures relying on these weak equivalences, for filtered complexes, multicomplexes and show that for spectral sequences we have a weaker notion of model category structure.