IMA, Minnesota, Sept. 8, 2004 Title: Stochastic conformal mapping and transport-limited aggregation Speaker: Martin Z. Bazant (Department of Mathematics, MIT, http://math.mit.edu/~bazant) Abstract: Conformal mapping provides elegant formulations of interfacial dynamics in two dimensions. Continuous conformal-map dynamics is well known for Laplacian growth, where the interfacial velocity is the gradient of a harmonic function, such as the pressure field in viscous fingering. Recently, stochastic Laplacian growth, which describes diffusion-limited aggregation and dielectric breakdown, has been formulated in terms of random, iterated conformal maps, by Hastings and Levitov (1998). Here, we extend these powerful analytical methods to a class of non-Laplacian growth phenomena, e.g. driven by advection-diffusion or electro-diffusion on flat or curved surfaces. As an example, we focus on the fractal aggregation of diffusing particles in a fluid flow.