##### Department of Mathematics,

University of California San Diego

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### Department Colloquium

## Alex Dunlap

#### NYU

## Stochastic partial differential equations 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.

Todd Kemp

### November 16, 2022

### 2:00 PM

APM 6402

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