On April 27, our institute invited Professor Xu Quanhua, a distinguished professor from the University of Franche-Comte, France, and a professor from Harbin Institute of Technology, to give a lecture entitled "Noncommutative Lp-spaces and applications" in Room 22515, which was hosted by our dean, Ding Yiming. Some faculty members and graduate students from the Department of Mathematics and Statistics attended the lecture. In this lecture, Professor Xu introduced the emerging interdisciplinary field of noncommutative analysis to the audience. This field is closely related to harmonic analysis, operator theory, quantum probability, and quantum information. Professor Xu began by introducing the construction process of classical Lp spaces, then introduced the mathematical foundation of quantum probability, and analyzed matrix systems from the perspective of case studies to obtain noncommutative measure spaces. He introduced how to extend classical Lp spaces to noncommutative Lp spaces in a simple and easy-to-understand manner, and detailed explained how to extend the research problems of classical cases to noncommutative cases by using the extension and proof of the Dunford-Schwartz maximum ergodic theorem as a case study.
After the report, the participating teachers and students actively participated in the discussion and had an in-depth academic exchange with Prof. Xu. Prof. Xu gave detailed answers to the questions raised, and the atmosphere was warm and academic.
Finally, the leaders and teachers present took a group photo with Prof. Xu.
This academic report not only brought new academic perspectives to our teachers and students and improved their academic literacy, but also inspired our teachers and students to think and explore more in the future scientific research path.
Personal profile: Xu Quanhua is a distinguished professor at Franche-Comté University in France and dean of the Institute of Mathematics of Harbin Institute of Technology. He received his Ph.D. in 1988 under the supervision of Gilles Pisier, a well-known expert in functional analysis and a member of the French Academy of Sciences. In 2014, Professor Xu Quanhua was elected as a Senior Research Fellow at the Graduate School of the University of France. He is recognized as one of the founders of modern non-commutative martingale theory in the mathematical community, and has published more than 80 papers in top international mathematical journals such as JAMS, JFA, GFA, TAMS, Crelles, etc. In 1997, he and Academician Gilles Pisier were the first to achieve breakthrough results in the field of noncommutative martingale theory and non-commutative ergodic theory. Subsequently, in 2007, Marius Junge and Marius Junge demonstrated the noncommutative maximal ergodic inequality, solving a nearly 30-year-old public problem in quantum probability. In 2010, he and Marius Junge constructed an important quantum probability method in operator space theory. In addition, Prof. Xu Quanhua also established the Littlewood-Paley theory of Grothendieck inequalities and vector values of non-commutative Lp spaces under the framework of operator space.
