Given a set K in R^2 with Hausdorff dimension t \in [0, 2], what can we say about a typical orthogonal projection of K? Marstrand (1954) proved that for Lebesgue almost all unit vectors \theta \in S^1, the dimension of the projection \pi_\theta (K) to \theta is min{t, 1}. To refine the question, we can replace Lebesgue measure with an s-dimensional Frostman measure \nu for s \in (0, 1], and ask for the dimension of typical projections \pi_\theta (K) for \theta in the support of \nu. We give an essentially sharp answer to this question, drawing on deep connections to harmonic analysis and geometric measure theory. Joint works with Yuqiu Fu and Hong Wang.Speaker’s website: https://kevinren-math.github.io/

Speaker’s website: https://kevinren-math.github.io/