Geometry of Laplacian growth models

Abstract

The project addresses various questions at the interface of probability, geometry and statistical mechanics, whose common feature is novel assertion of physical phenomenon in natural probabilistic models. The specific problems are concerned with complex systems, that are generated by diffusion, or the harmonic measure, such as aggregation processes, in an attempt to grasp the nature of a physical phenomenon, which is resisting proof in more classical models in the field, such as DLA. The problems concentrate around the Hastings-Levitov model, which is a continuous off lattice version of many of the known lattice aggregation models. The methods to be employed borrow ideas and tools from various mathematical disciplines e.g. complex analysis, harmonic analysis, differential equations, ergodic theory and geometric measure theory. The project contains problems whose difficulty ranges from graduate to full research level. It therefore offers a great opportunity to get graduate students and postdocs involved in top-notch research in probability and mathematical physics. The project will also aid to continue the tradition of the PIs' collaborative involvement with the international community. (AU)