Interacting Particle Systems and Mean-field games Workshops

Brown University, Providence RI

Investigators

Abstract

This project will support participation of graduate students, post-doctoral researchers and early career researchers from the United States of America in one of the workshops "Interacting Particle Systems and Hydrodynamic Limits" to be held from March 13-27, 2022, or the "Mean-Field Games" workshop to be held from April 10-17, 2022 at the Centre de Recherches Mathematiques (CRM) in Montreal, Canada. Both workshops are part of a larger interdisciplinary thematic program on "Probabilities and PDEs" held at CRM from January to July 2022. Probability theory and the theory of partial differential equations (PDEs) are important areas of mathematics with substantial overlap in their methods and goals. In both fields, one of the major aims is to provide accurate models of how engineered, physical, chemical and biological systems change over time. Probability frequently focuses on how systems which are random and/or unpredictable at the microscopic level can become highly ordered at the macroscopic level. PDE theory frequently focuses on the spatial and temporal evolution of such macroscopic systems. For decades there has been a fruitful interplay between the two fields probability and PDEs, with both intuitions and mathematical techniques from each area finding application in the other. This project focuses on two aspects of that interplay, which are both related to how probabilistic particle systems resemble PDEs when sufficiently "zoomed out". One of these, the area of mean-field games, describes scaling limits of strategically controlled interacting agents evolving as diffusions coupled via a graph structure (often the complete graph). The second, interacting particle systems and hydrodynamic limits, typically focuses on PDE approximations for particle systems in more geometric settings, such as lattices (on taking an appropriate fine-mesh limit in both space and time). The goal of this project is to support the participation of US-based junior researchers and researchers from underrepresented groups in a thematic semester on Probability and PDEs (and in particular their participation in two workshops, on the subjects of mean-field games and interacting particle systems), taking place in the first half of 2022 at the Centre de Recherches Mathématiques in Montréal, Canada. The thematic semester website is maintained at http://www.crm.umontreal.ca/2022/Probab22/index_e.php the Interacting Particle Systems and Hydrodynamic Limits Workshop at http://www.crm.umontreal.ca/2022/Particules22/index_e.php and the Mean-Field Games Workshop at http://www.crm.umontreal.ca/2022/Games22/index_e.php. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.