Emerging Synergies between Stochastic Analysis and Statistical Mechanics (25w5367)

The Banff International Research Station will host the “Emerging synergies between stochastic analysis and statistical mechanics” workshop in Banff from October 26 - 31, 2025.

In recent decades, Stochastic Partial Differential Equations (SPDEs) have become a dynamic field at the intersection of stochastic analysis and statistical mechanics. In the late 1980s and 1990s, systematic theories for analysis of SPDEs emerged, such as Walsh's probabilistic framework based on martingale measures, Da Prato and Zabczyk's semigroup-based approach, and theories based on weak or martingale solutions and Dirichlet forms. In a remarkable paper, Kardar, Parisi, and Zhang (KPZ) introduced a nonlinear SPDE to depict the behavior of a growing interface subjected to random disturbances. In 1997, Bertini and Giacomin's showed that the solution to the transformed KPZ equation serves as the macroscopic limit of specific interacting particle systems. This discovery marked the initial rigorous confirmation of the existence of the KPZ universality class, and opened up a dynamic area of research connecting particle systems, random matrices, and other fields. Until the early 21st century, many complex SPDEs posed significant challenges for mathematical analysis due to their singular nature, closely tied to irregularities in the underlying random data. In 2013, a major breakthrough occurred when Hairer developed a framework for solving the KPZ equation, drawing on concepts from Lyons' rough paths theory, marking a significant advance in understanding singular equations.

The workshop will contribute to the advancement of the rapidly growing theory of SPDEs, leading to fundamental new impulses for the field. Its first goal is to bring together internationally renowned researchers working at the interface between stochastic analysis and statistical mechanics, to interact, exchange recent results, establish new collaborations, and generate novel ideas for research directions. The second goal is to provide a platform for junior researchers to present their work in an environment that cultivates collaborations, to provide them with networking opportunities, and to help them find inspiration. Recognizing the significance of nurturing young talent, the workshop aims to play a pivotal role in inspiring the next generation of researchers, and have a long-lasting impact on their careers.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada’s Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), and Alberta’s Advanced Education and Technology.