The boundary of the support of super-Brownian Motion

We will study the edge of the support of 1-dimensional super-brownian motion. The local behaviour of the density, Hausdorff dimension of the boundary, and rates of convergence of certain solutions to singular semilinear heat equations studied in the pde literature are all expressed in terms of a particular eigenvalue of a killed Ornstein-Uhlenbeck operator. Time permitting, we will discuss some possible connections with pathwise uniqueness questions for some related stochastic pde's. This is joint work with Carl Mueller and Leonid Mytnik.