American Institute of Mathematics, Palo Alto, California
Ivan Corwin and Jeremy Quastel
This workshop, sponsored by AIM and the NSF, will be devoted to the study of the the Kardar-Parisi-Zhang equation and universality class.
Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its continuum properties (such as distribution functions) and expanding the breadth of its universality class. Recently, a new universality class has emerged to describe a host of important physical and probabilistic models (such as one dimensional interface growth processes, interacting particle systems and polymers in random environments) which display unusual scalings and new statistics. This class is called the Kardar-Parisi-Zhang (KPZ) universality class and underlying it is, again, a continuum object -- now a non-linear stochastic partial differential equation -- which is known as the KPZ equation.
The purpose of this workshop is to build on recent successes in understanding the KPZ equation and its universality class. There are two main focuses:
The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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