Title: Stochastic partial differential equations in supercritical, subcritical, and critical dimensions
Abstract: A pervading question in the study of stochastic PDE is how small-scale randome forcing in an equation combines to create nontrivial statistical behavior on large spatial and temporal scales. I will discuss recent progress on this topic for several related stochastic PDEs - stochastic heat, KPZ, and Burgers equations - and some of their generalizations. These equations are (conjecturally) universal models of physical processes such as a polymer in a random environment, the growth of a random interface, branching Brownian motion, and the voter model. The large-scale behavior of solutions on large scales is complex, and in particular depends qualitatively on the dimension of the space. I will describe the phenomenology, and then describe several results and challenging problems on invariant measures, growth exponents, and limiting distributions.
Bio: Dr. Dunlap received his PhD from Stanford University in 2020 and is currently an NSF Postdoctoral Fellow at New York University.
For those that will be unable to attend this talk in person, a Zoom link is available: https://illinois.zoom.us/j/87568029137?pwd=bi8yU0JNaEg0SCtpaG9VdnpST2tEUT09&from=addon
