The Kardar-Parisi-Zhang Equation and its Universality Class

Jeremy Quastel, University of Toronto
Fine Hall 314

The KPZ equation was introduced in 1986, and has become the default model in physics for random interface growth. It is a member of a large universality class with non-standard fluctuations, including directed random polymers. Even in one dimension, it turned out to be difficult to interpret and analyze mathematically, but at the same time to have a large degree of exact solvability. We will survey the history and recent progress.