February 24-March 2, 2013

Organizers: Alexei Borodin, Jeremy Quastel, Herbert Spohn

The Kardar-Parisi-Zhang equation is a nonlinear stochastic partial differential equation widely used in the physics literature as a model of randomly growing interfaces, but until recently very poorly understood from the mathematical point of view. In one dimension, it is a member of a large universality class containing directed random polymers, stochastic Hamilton-Jacobi-Bellman equations, stochastically perturbed reaction-diffusion equations, stochastic Burgers equations and interacting particle models. The class is characterized by the unusual dynamic scaling exponent z=3/2. A number of breakthroughs about 10 years ago led to exact distributions of fluctuations for a few models, with conjectural extrapolation to the whole class. The distributions, surprisingly, turned out to be those recently discovered in random matrix theory. In the last few years there have been a second group of breakthroughs. Several models with adjustable asymmetry have recently been solved through which one can obtain, by scaling limits, exact distributions for various initial conditions for the KPZ equation itself. In addition, there have been breakthroughs in the well-posedness of the KPZ equation.

The goal of this workshop is to build on these advances in two directions. 1. Studying the integrability properties and statistics of the KPZ equation, as well as other models in the KPZ universality class. 2. Extending the universality of the KPZ equation. The new well-posedness theory should provide a route to proving scaling limits to the KPZ equation for a wider class of physical models.

**Participants**

Fedor Bogomolov, *NYU/Courant*

Mark Adler, *Brandeis University*

Gerard Ben Arous, *NYU/Courant*

Alexei Borodin, *MIT*

Pasquale Calabrese, *Universita di Pisa*

Reda Chhaibi, *Universitat Zurich*

Ivan Corwin, *MIT/Microsoft Research*

Percy Deift, *NYU/Courant*

Victor Dotsenko, *University of Paris 6*

Patrik Ferrari, *University of Bonn*

Alan Hammond, *University of Oxford*

Kurt Johnasson, *KTH*

Kostya Khanin, *University of Toronto*

Pierre Le Doussal, *ENS, Paris*

Pierre van Moerbeke, *Université catholique de Louvain*

Neil O’Connell, *Warwick University*

Jeremy Quastel, *University of Toronto*

Tomohiro Sasamoto, *Chiba University*

Timo Seppalainen, *University of Wisconsin-Madison*

Senya Shlosman, *University of Marseilles*

Herbert Spohn, *Technische Universitat Munchen*

Craig Tracy, *UC Davis*

Jon Warren, *Warwick University*