The critical 2-d Stochastic Heat Flow and some of its properties

The critical 2-d Stochastic Heat Flow arises as a non-trivial solution of the Stochastic Heat Equation (SHE) and its discretisation via directed polymers at the critical dimension 2 and at a phase transition point. It is a log-correlated field, which is neither Gaussian nor a Gaussian Multiplicative Chaos. We will review the phase transition of the 2-d SHE, describe the main points of the construction of the Critical 2-d SHF and outline some of its features (e.g. singularity, regularity, moments, support etc.) Most of the talk will be based on joint works with Francesco Caravenna and Rongfeng Sun but contributions of other researchers will be presented.