Zoom link.

https://msri.zoom.us/s/585445592

Multicomplexes (also known as twisted complexes) are a generalization of  bicomplexes introduced by Wall in the sixties, and frequently encountered in different contexts. They yield to filtered complexes, then to spectral sequences, and thus to a family of weak equivalences, called E_r-equivalences: a morphism f of multicomplexes is an E_r-equivalence if it is an isomorphism at the r+1-stage of the associated spectral sequence. In joint works with Sarah Whitehouse, Joana Cirici, Daniela Egas Santander and with Xin Fu and Ai Gan, we proved that there is a cofibrantly generated model category structure on multicomplexes with weak equivalences being E_r-equivalences. The purpose of the talk is to motivate this work, give some details on the constructions and proof, and present some work in progress.

Homotopy Theories Of Multi Complexes