Weak Universality for KPZ with general nonlinearity and Poisson noise

We consider a class of weakly asymmetric continuous microscopic growth models with polynomial smoothing mechanisms, general nonlinearities and a Poisson type noise. We show that they converge to the KPZ equation after proper rescaling, where the coupling constant depends on all details of the smoothing and growth mechanisms in the microscopic model. This provides a first example of Hairer-Quastel type with both generic nonlinearity and non-Gaussian noise. This talk is based on the joint work with Haiyi Wang and Weijun Xu.