Academic Report of School of Mathematical Sciences [2025] No. 109

(Series Report for High-Level University Construction No. 1211)

Title: Harmonic Analysis of Multiplicative Chaos

Speaker: Researcher Qiu Yanqi (Hangzhou Institute for Advanced Study, UCAS)

Time: 16:30-17:30, November 9, 2025 (Sunday)

Location: Office Area 1413, Huiwen Building

Abstract:

I will introduce a general method for dealing with the Fourier decay of random measures arising from Kahane's T-martingale theory, thus including Mandelbrot Cascades (canonical or microcanonical), Gaussian Multiplicative Chaos, Random Coverings, and more abstract ones. This very new method combines many fundamental vector-valued martingale inequalities, such as Pisier's martingale type inequality, the Burkholder-Rosenthal inequality, the Bourgain-Stein inequality, etc., and also incorporates an idea seemingly related to the decoupling method in harmonic analysis. The talk is based on joint works with Xinxin Chen, Yong Han, Zipeng Wang; with Zhaofeng Lin, Mingjie Tan; and with Yukun Chen, Zhaofeng Lin.

Speaker Profile:

Qiu Yanqi is a Researcher at the Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences. His research interests include probability theory, ergodic theory, random matrices, harmonic analysis, and functional analysis.

All faculty and students are welcome!

Host: Han Yong

School of Mathematical Sciences

November 5, 2025