Scaling Limits of Planar Random Growth Models

Amanda Turner, University of Leeds. Part of the Leeds Applied Nonlinear Dynamics seminar series.

Speaker: Amanda Turner, University of Leeds

Title: Scaling Limits of Planar Random Growth Models

Abstract: Planar random growth processes occur widely in the physical world. Examples include diffusion-limited aggregation (DLA) for mineral deposition and the Eden model for biological cell growth. One approach to mathematically modelling such processes is to represent the randomly growing clusters as compositions of conformal mappings in the complex plane. In 1998, Hastings and Levitov proposed one such family of models, which includes versions of the physical processes described above, but there are many natural generalizations. In this talk I will give a survey of the main results and conjectures in this area.