Quantum Fourier Analysis

讲座时间 Datetime: 2022年6月27日，星期一，10:00—11:30

地点 Venue: 腾讯线上会议：961-750-600

主持人 Host：张汉斌

报告人 Speaker: 黄林哲

单位 Affiliation:清华大学

报告摘要 Abstract:

Quantum Fourier Analysis is a theory of studying quantum symmetries, focusing on the analytic, algebraic and topological properties of quantum Fourier duality. In this talk, I will introduce the background and recent progress in quantum Fourier analysis. It contains three parts: (1) Quantum uncertainty principles on quantum symmetries in quantum Fourier analysis. We studied the quantum Widgeson-Widgeson uncertainty principles and answered the open question proposed by them. (2) Demonstrate how to apply the tools of quantum Fourier analysis to solve the categorification problems of fusion rings through examples. (3) Quantum Perron-Frobenius theorem and graphical interpretation. It is a joint work with Zhengwei Liu and Jinsong Wu.

Reference：

[1] A. Jaffe, C. Jiang, Z. Liu, Y. Ren, J. Wu, Quantum Fourier Analysis, PNAS, 2020 117(20), 10715-10720

[2] L. Huang, Z. Liu, J. Wu, Quantum Smooth Uncertainty Principles for von Neumann bi-algebras arxiv:2107.09057

[3] L. Huang, Z. Liu, J. Wu, Quantum convolution inequalities on Frobenius von Neumann algebras arXiv:2204.04401