Dimension and Dynamics

This ambitious project tackles several fundamental questions in dynamical systems, additive combinatorics, and probability theory by developing groundbreaking techniques. These new techniques are rooted in fractal geometry and will make use of the latest developments in dimension theory. In particular, we will tackle the dimension drop conjecture, advance our understanding of projections of regular sets, and aim to resolve open questions on quasi-symmetric embeddings of random metric spaces. Our approach is to develop unifying machinery that will help in studying these seemingly disparate questions.