Organizers
Jian Ding (丁剑), Peking University
Xicheng Zhang (张希承), Beijing Institute of Technology
Xiangchan Zhu (朱湘禅), Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Chenlin Gu (顾陈琳), Tsinghua University
Wenbo Li (李文博), Tsinghua University
Abstract
Random walks and stochastic differential equations are core pillars of probability theory, and their intersection and integration are driving cutting-edge breakthroughs in modern mathematics and related fields. This workshop aims to bring together scholars to focus on the most dynamic research directions and engage in in-depth discussions on major advances and core challenges in this area.
The conference will revolve around the following key themes: In the realm of stochastic partial differential equations, we will focus on the homogenization of singular SPDEs to understand macroscopic behavior in random media, as well as the weak universality of the KPZ equation, exploring its universality class beyond classical integrable systems and its profound connections to random matrices and two-dimensional Anderson localization. In the asymptotic theory of random walks, we will conduct an in-depth analysis of the geometry and large deviations of branching random walks, and investigate the scaling limits of random walks on critical long-range percolation, revealing the fundamental impact of critical phenomena on walk behavior. Furthermore, the conference will explore the regularizing effects of stochastic systems, specifically the mechanism of regularization by noise, as well as the phenomena of anomalous dissipation and enhanced dissipation in fluid dynamics and transport theory. Finally, attention will be given to random walks on level sets of Gaussian free fields, a direction linking deep questions in random geometry, potential theory, and statistical physics.
This workshop is an academic activity supported by the Major Program of the National Natural Science Foundation of China "Theoretical Exploration of Stochastic Phenomena in Mathematical Physics." It will not only showcase profound advances within probability theory but also aim to reveal its connection to statistical physics and partial differential equations, fostering collaborative innovation across these interdisciplinary fields.
