Infinite Dimensional Double Backward SDE and KPZ Equation

The Kardar-Parisi-Zhang(KPZ) equation is a stochastic partial differential equation driven by space time white noise proposed as the scaling limit for random growth models in physics. The solution of this equation is interpreted as the height of a dynamically evolving surface. So far, the solution to this ill posed equation has been understood as a limit of a system of interacting particles. In this talk we will review the basic facts of these constructions, including the so called universality conjectured. We then propose a new form of understanding the solution by posing an infinite dimensional stochastic differential equation driven by a brownian sheet and by a brownian motion backward in time. We show that our construction is consistent with the interacting particle system approach.