Georgia Institute of Technology College of Sciences

The Kardar-Parisi-Zhang(KPZ) equation is a non-linear stochastic partial di fferential equation proposed as the scaling limit for random growth models in physics. This equation is, in standard terms, ill posed and the notion of solution has attracted considerable attention in recent years. The purpose of this talk is two fold; on one side, an introduction to the KPZ equation and the so called KPZ universality classes is given. On the other side, we give recent results that generalize the notion of viscosity solutions from deterministic PDE to the stochastic case and apply these results to the KPZ equation. The main technical tool for this program to go through is a non-linear version of Feyman-Kac's formula that uses Doubly Backward Stochastic Differential Equations (Stochastic Differential Equations with times flowing backwards and forwards at the same time) as a basis for the representation.