AQFTs vs. Factorization Algebras: toward a higher comparison

Quantum Field Theory (QFT) is an exciting yet elusive domain within mathematics and physics. Despite the lack of rigorous foundations to support many advancements made by physicists, mathematicians have engaged in a fruitful endeavor to formalize QFTs. In current times, we find ourselves at a crossroads: while we still lack the comprehensive techniques and language to fully grasp QFT, numerous distinct axiomatic frameworks are attempting to capture its essence. A natural question arises: how are these approaches connected? This talk will focus on two such frameworks: Algebraic Quantum Field Theories (AQFTs) and Factorization Algebras (FAs). The significance of these frameworks is motivated, among other things, by rigorous programs led by Fredenhagen-Rejzner and Costello-Gwilliam to construct perturbative QFTs using AQFTs and FAs, respectively. Recent contributions from Gwilliam-Rejzner and Benini-Musante-Schenkel establish a relationship between these two programs, vaguely speaking. At a more structural level, Benini-Perin-Schenkel have established an equivalence of 1-categories between specific subcategories of AQFTs and (time-orderable pre-)FAs. The goal of this talk is to present our strategy for establishing an even broader equivalence between ∞-categories of AQFTs and tpFAs.