Special Colloquium / Alexander Dunlap (New York University)
- Event Type
- Seminar/Symposium
- Sponsor
- Renming Song
- Location
- 245 Altgeld Hall
- Date
- Nov 15, 2022 4:00 pm
- Contact
- Renming Song
- rsong@illinois.edu
- Views
- 7
Title: Stochastic partial differential equasions in supercritical, subcritical, and critical dimensions.
Abstract: A pervading question in the study of stochastic PDE is how small-scale random 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.