Time-dependent averages of a critical long-range stochastic heat equation

In this talk we will first introduce a special case of a long-range linear stochastic heat equation which is borderline critical. We will discuss the solution theory which dates back to 2004 work of Mueller and Tribe. We will then talk about the time-dependent spatial averages and the limiting behavior on different scales. The latter part of this talk is based on a joint work in progress with Ran Tao.