Stochastic heat flow: axiomatic formulation and applications

The Stochastic Heat Flow (SHF) emerges as the scaling limit of directed polymers in random environments and the noise-mollified stochastic heat equation, specifically at the critical dimension of two and near the critical temperature. I will present an axiomatic formulation of the SHF as well as its construction based on its moments, and discuss how this formulation can be applied to solve a range of problems.