On September 11, Academician Marcelo Viana, Director of the Institute for Pure and Applied Mathematics (IMPA) in Brazil and Chair of the International Congress of Mathematicians (ICM) Organizing Committee, delivered a distinguished lecture titled "Repellers of Random Walks" at Beihang University.

The event attracted over 200 faculty members and students from more than ten schools and colleges across the university, including the School of Mathematical Sciences, Shen Yuan Honors College, and the School of Artificial Intelligence. The lecture was also livestreamed via the Virtual Teaching and Research Platform for the "Hua Luogeng Mathematics Experimental Program," a key initiative for training top-tier mathematical talents. The online broadcast drew widespread participation from students and scholars at over 20 institutions, including Peking University, Tsinghua University, the Chinese Academy of Sciences, and Beijing Normal University.

In his presentation, Academician Viana addressed the longstanding question of the continuity of Lyapunov exponents in random walks. By analyzing random walks, Markov operators, and stationary measures, he demonstrated that Lyapunov exponents are in fact continuous—a result that resolves a major challenge in the field. His findings provide deeper insight into the stability of random linear systems and hold significant implications for the intersection of dynamical systems and probability theory.

Prior to the lecture, Vice President Deng Yi presented Academician Viana with an honorary certificate of "Beihang Grand Lecture" in recognition of his academic leadership and contributions.

The lecture was met with enthusiastic engagement, fostering a vibrant atmosphere of intellectual exchange. Following the presentation, many students actively engaged in in-depth discussions with Academician Viana about various challenges and ideas in mathematical research. He patiently addressed each query and encouraged students to remain curious, think independently, and embrace challenges with courage. He emphasized the importance of perseverance, intellectual ambition, and the willingness to ask new questions and explore uncharted directions in the pursuit of academic dreams.

Marcelo Viana is a Member of the Brazilian Academy of Sciences and a Fellow of The World Academy of Sciences (TWAS). He has served as Vice President of the International Mathematical Union (IMU), President of the Brazilian Mathematical Society, and Chair of the Organizing Committee for the 2018 International Congress of Mathematicians. Viana has been engaged in long-term research in the fields of dynamical systems and ergodic theory, achieving significant results. He has published over 80 papers in top-tier journals such as Annals of Mathematics, Acta Mathematica, and Inventiones Mathematicae. He is a recipient of the Ramanujan Prize and the TWAS Prize, and was an invited speaker at the ICM both in 1994 (45-minute lecture) and 1998 (plenary address).

Editor: Lyu Xingyun