Title: Algebraic models of spaces
Abstract: It is known that E_∞ cochains completely capture localizations of simply connected spaces subject to certain finiteness conditions. This is due to Quillen-Sullivan in the rational case, and Mandell in the p-adic case. However, the embedding into Z-valued cochains turns out to be faithful but not full. The subject of finding an algebraic model for integral homotopy types has seen significant progress in the past few years. We now have several fully faithful embeddings of simply connected finite complexes into "algebraic" ∞-categories. In this talk, I will introduce two approaches due independently to Yuan and Horel.