Conference: CRM Thematic Semester Spring 2022: Probabilities and PDEs

该项目将支持来自美国的研究生、博士后研究人员和早期职业研究人员参加将于2022年5月2日至13日在加拿大蒙特利尔数学研究中心举行的“分支系统、反应扩散方程和人口模型”或2022年5月16日至27日在加拿大蒙特利尔数学研究中心举行的“统一随机偏微分方程（PDEs）的概念”研讨会。数学模型和概率之间的相互作用是丰富而深刻的，其应用遍及所有科学领域。这种相互作用可以出现在材料科学和流体动力学的许多物理环境中，也可以出现在各种多媒介或多粒子动力学的建模中，例如生物体的自组织运动或传染病在种群中的传播。在2022年1月至2022年7月期间，mathacimmatiques研究中心正在组织一个关于这一主题的密集专题方案，即“概率和pde”。将有四个研讨会，每个研讨会都有专门针对研究生或相关领域的早期职业研究人员以及许多长期访问科学家的迷你课程。该奖项提供资金，支持美国研究生、早期职业研究人员和代表性不足的少数民族参加两个研讨会之一的旅行和住宿以及附带的迷你课程。这将为参与者提供一个绝佳的机会，与彼此和该领域的领导者进行互动，并将帮助他们了解该领域的主要问题并学习该领域的前沿方法。概率和偏微分方程一直是相互交织的，现代研究继续将它们进一步交织在一起。一个共同的方面是如何通过随机初始数据、随机环境、随机强迫等方式将随机性引入偏微分方程，这将深刻地影响长期行为，因为它为研究物理模型提供了一种灵活而现实的方法，或者因为它是底层系统模型的不可避免的特征。另一个方面是如何从潜在的随机多主体或多问题中获得确定性偏微分方程，例如在经典动力学理论或数学流行病学等多主体问题中。该项目将把世界各地的专家和初级研究人员聚集在一起，进行一个密集而集中的项目，这将有助于极大地促进对这些现象的理解，该奖项将有助于在这些方法方面培训下一代美国科学家。主题学期网站是http://www.crm.umontreal.ca/2022/Probab22/index_e.php分支系统，反应扩散方程，和人口模型研讨会（网址：http://www.crm.umontreal.ca/2022/Systemes22/index_e.php），以及将pde的概念与随机性结合起来的研讨会（网址：http://www.crm.umontreal.ca/2022/Concepts22/index_e.php.This）反映了国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.