Speaker：Yixiao Qiao (Guangdong University of Technology)

Time：2024-3-15, 10:30

Location：Conference Room 110 at Experiment Building at Haiyun Campus

Abstract:

In this talk I shall address an embedding problem in relation to mean dimension theory, which concerns the connection between embedding possibility and mean dimension at a critical value for minimal dynamical systems. I will present its historical background briefly, and give a complete solution to this problem. More precisely, we prove that the shift action on the Hilbert cube contains a minimal subshift of full mean dimension. In contrast to dimension theory and entropy theory, this is a different phenomenon in mean dimension theory. The proof is constructive. Our result, in company with all the previously known results in this direction, leads eventually to a full understanding of the embedding possibility of minimal dynamical systems in Hilbert cubes with a view towards mean dimension. This is a joint work with Lei Jin.