Abstract:
I will discuss recent progress in the study of the 2-dimensional stochastic heat equation (SHE) and the Kardar-Parisi-Zhang (KPZ) equation, which are critical singular stochastic partial differential equations (SPDEs) that lie beyond existing solution theories. Both the 2D SHE and KPZ undergo a phase transition, and the solution of the 2D SHE at the critical point leads to the so-called critical 2D stochastic heat flow. This provides a rare example of a model in the critical dimension and at the critical point with a non-Gaussian limit. Our approach is motivated by the scaling limits of disordered systems, in particular, the directed polymer model in random environment for which disorder is marginally relevant in 2D. Based on joint work with F. Caravenna and N. Zygouras.
Biography:
Rongfeng Sun obtained his Ph.D. from New York University in 2004. He was a postdoc in EURANDOM, TU Eindhoven, from 2004-2006, and a postdoc in TU Berlin from 2006-2008. He then joined the National University of Singapore, where he is currently a professor. His research interests are in probability theory, and in particular, in interacting particle systems, statistical mechanical models, and their scaling limits.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.