As a vital branch of mathematics, probability theory plays a crucial strategic role in modern scientific and technological advancement. It not only serves as a cornerstone for foundational mathematical theories such as measure theory and real analysis, but also provides essential support for applied mathematical disciplines including statistics, information theory, and operations research. Probability theory finds wide application across fields such as the natural sciences, engineering, economics, and finance. In emerging areas like artificial intelligence and big data analytics, probabilistic models have become core tools for addressing uncertainty. The deepening of probabilistic theory and its expanding applications are of paramount importance in driving an intelligent future.
Recently, a frontier seminar on probability theory, meticulously organized by Professor Liu Wei and aimed at outstanding undergraduates, was successfully held. Nearly thirty students participated, and the discussions were lively and engaging. The first session focused on Stein’s method and its applications. It aimed to solidify undergraduates’ theoretical foundations in probability theory, introduce them to its research frontiers, inspire scientific curiosity and innovative thinking, and cultivate future talents for artificial intelligence and related fields. Professor Liu emphasized the strategic position of probability theory within both pure and applied mathematics, particularly in building AI technologies. He also highlighted its close connections with cutting-edge AI research and Fields Medal–related studies, underscoring the academic value of probability theory.
The inaugural session was delivered by Fang Zijin, an undergraduate from the Class of 2022 in the Mathematics “Self-Strengthening” Program, under the title “Stein’s Method and Its Applications.” Fang systematically explained the origins, core ideas, and areas of application of Stein’s method, demonstrating a solid theoretical foundation. The presentation offered an in-depth analysis of how Stein’s method achieves distributional approximation through expectation control and provided a detailed discussion of various metrics for measuring distances between random variables—such as total variation distance and Kolmogorov distance—defined based on test functions. Fang also clarified the internal relationships among these metrics and their respective use cases. Her presentation was clear, accessible, and informative, laying a strong foundation for understanding Stein’s method. During the two-and-a-half-hour lecture, Fang spoke without relying on notes, showcasing both her command of the material and her academic enthusiasm, earning widespread praise from both faculty and students.
The successful organization of this seminar fully reflects the School’s sustained commitment and remarkable achievements in fostering undergraduate research capacity. By hosting high-level academic seminars, the School provides students with a valuable platform to engage in in-depth exchanges with experts in the field, effectively enhancing their research literacy. Such activities inspire students’ academic interests and foster critical thinking and creative abilities. Professor Liu noted that the seminar series will continue throughout the year, focusing on international frontier topics in probability theory, emphasizing solid theoretical foundations, and guiding students to explore scientific frontiers, broaden their academic horizons, and embark on their research journey. The seminar will also actively invite more renowned scholars from China and abroad to participate, jointly exploring cutting-edge issues in probability theory. The ultimate goal is to build the seminar into a high-level platform that inspires research enthusiasm, cultivates innovative thinking, and promotes academic exchange, thereby making a positive contribution to the School’s mission of cultivating first-class talent.
