Topic: Box and packing dimensions of orthogonal projections of Gatzouras-Lalley carpets and phase transitions

Lecturer: Prof. De-Jun Feng, The Chinese University of Hong Kong

Time: March 17, 2026, 16:00, UTC+8

Venue: Room 213, Mathematics and Statistics Building

Biography: De-Jun Feng is a Professor in the Department of Mathematics at The Chinese University of Hong Kong. He has made a series of groundbreaking contributions in multifractal analysis, the dimension theory of invariant measures for iterated function systems, mathematical principles of thermodynamic formalism, and rigidity of self-similar structures. He has published over 80 papers in prestigious journals such as Duke Math. J., CPAM, GAFA, JEMS, Ann. Probab., and Adv. Math. He is a leading international expert in the fields of fractal geometry and dynamical systems.

Abstract: The study of orthogonal projections of sets and measures is an important topic in geometric measure theory. Two decades ago, Falconer and Howroyd established the projection theorems for the packing, and upper and lower box dimensions. They showed that for every Borel set A in ℝᵈ, each of the packing, upper box and lower box dimensions of the projection Pᵥ(A) of A takes a constant value, which can be expressed as a certain dimension profile, for almost all k-dimensional subspaces V. However, these dimension profiles are typically very difficult to compute. Recently, we have succeeded in obtaining the precise values of these dimension profiles for homogeneous Gatzouras-Lalley carpets, which exhibit remarkable phase transitions. The talk is based on joint work with Caiyun Ma and Karoly Simon.

Rewritten by: Li Huihui

Edited by: Li Tiantian

Source: School of Mathematics and Statistics