Professor David Jerison
PROFESSOR OF MATHEMATICS, MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Internal Diffusion-Limited Aggregation
In 1986, chemists Paul Meakin and John Deutch proposed a model for the process of removal of material such as occurs in electropolishing, erosion and etching. Their model, known as internal diffusion-limited aggregation or internal DLA, is a random model in which corrosive fluid is represented as a growing blob of lattice sites that eats away at its solid surroundings as it grows. The main question is, how smooth is the boundary of the blob? To answer this question we'll need partial differential equations, Fourier series, martingales, and methods used in analytic number theory to count the number of lattice points in a disk or ball.