Classical solutions of linear partial differential equations (PDEs) can be constructed by integrating Brownian motion. Many are familiar with this phenomenon in the context of the physical process of diffusion that can be studied with discrete random walks but also continuously, with the Laplace operator. However, such an analogy breaks down when the equations are nonlinear. It has been nevertheless observed that many stochastic processes refer to some form of a nonlinear differential equation as their limiting object. One known example is the inviscid Burgers’ equation which appears in different contexts of mathematical physics but can also be found in limiting behaviour of discrete stochastic processes. We invite applications for a PhD candidate who will investigate how nonlinear PDEs may be studied by complex stochastic processes, such as coalescence and branching. The position is fully funded for 4 years, with a preferable start in the fall of 2021.