• Bingyang Hu
• Assistant Professor
• Auburn University
• Date: Aug. 26, Wednesday, 2026
• Time: 14:00-15:15
• Host: Le Chen
• Room: STEM Ag 2111
• Video: Watch this talk on YouTube
• Abstract: The goal of this talk is to present a non-testing characterization of the boundedness and compactness of composition operators acting on \(Q_p\) spaces. This resolves an open problem posed in Xiao's 2001 book and settles the diagonal case of a broader problem raised by Zhao in 2009, one of the longest-standing open problems in the theory of Möbius-invariant function spaces. The main new ingredient is a reformulation of this complex-analytic problem as a dyadic trace problem, making it possible to bring tools from dyadic harmonic analysis and probability into play. I will also discuss further applications of the ideas underlying this dyadic trace theorem, which leads to solutions of several other open problems in complex function theory. This talk is based on several recent joint works with Xiaojing Zhou, including one joint work with Jie Xiao and Shuaibing Luo.

Recorded for the SASA YouTube channel, with the speaker's consent.