A forward-backward SDE from the 2D nonlinear stochastic heat equation

I will discuss a two-dimensional stochastic heat equation in the weak noise regime with a nonlinear noise strength. I will explain how pointwise statistics of solutions to this equation, as the correlation length of the noise is taken to 0 but the noise is attenuated by a logarithmic factor, can be related to a forward-backward stochastic differential equation (FBSDE) depending on the nonlinearity. In the linear case, the FBSDE can be explicitly solved and we recover the log-normal behavior proved by Caravenna, Sun, and Zygouras. Joint work with Yu Gu (CMU).