Conference: CRM Thematic Semester Spring 2022: Probabilities and PDEs

University Of Maryland, College Park, College Park MD

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 "Branching systems, reaction-diffusion equations, and population models" to be held May 2–13, 2022 or "Unifying concepts in partial differential equations (PDEs) with randomness" to be held May 16–27, 2022 at the Centre de Recherches Mathematiques (CRM) in Montreal, Canada. The interplay between mathematical models and probability is rich and profound with applications far-reaching across all fields of science. This interplay can appear in many physical settings in materials science and fluid dynamics, but also in the modeling of various many-agent or many-particle dynamics, such as the self-organized motion of organisms or the spread of an infectious disease through a population. The Centre de Recherches Mathématiques is organizing an intensive thematic program on this topic, "Probabilities and PDEs" during the period January 2022 -- July 2022. There will be four workshops, each with mini courses specifically aimed at graduate students or early-career researchers in related areas, and many long-term visiting scientists as well. This award provides funding to support the participation of US-based graduate students, early career researchers, and under-represented minorities through travel and accommodation during one of the two workshops and accompanying mini-courses. This will provide the participants with a perfect opportunity to interact with each other and with leaders of the field and will help them to understand the major questions and learn the cutting-edge methods of the field. Probability and PDEs have always been intertwined and modern research continues to intertwine them further. One common aspect concerns how introducing randomness into PDEs, through e.g. random initial data, random environments, random forcing will profoundly affect the long-term behavior, either because it provides a flexible and realistic approach to study physical models or because it is an inevitable feature of models of the underlying systems. Another aspect is how one can obtain deterministic PDEs from underlying random many-agent or many-problems, such as in classical kinetic theory or in many-agent problems such as in mathematical epidemiology. The program will bring together world experts and junior researchers in an intensive and focused program that will help to greatly further the understanding of these phenomena and this award will help train the next generation of US-based scientists in these methods. The thematic semester website is maintained at http://www.crm.umontreal.ca/2022/Probab22/index_e.php the Branching systems, reaction-diffusion equations, and population models workshop at http://www.crm.umontreal.ca/2022/Systemes22/index_e.php and the Unifying concepts in PDEs with randomness workshop at http://www.crm.umontreal.ca/2022/Concepts22/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.