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日举行的“分支系统，反应扩散方程和人口模型”研讨会之一，或将于5月16日至27日举行的“随机偏微分方程（PDE）中的统一概念”，2022年在加拿大蒙特利尔的数学研究中心（CRM）。数学模型和概率之间的相互作用是丰富而深刻的，其应用范围遍及所有科学领域。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代理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人群中的传播。数学研究中心正在组织一个关于这个主题的密集主题计划，“概率和偏微分方程”在2022年1月至2022年7月期间。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的迷你课程，以及许多长期访问的科学家。该奖项提供资金，以支持美国的研究生，早期职业研究人员和代表性不足的少数民族通过旅行和住宿期间的两个研讨会和伴随的迷你课程之一的参与。这将为参与者提供一个完美的机会，相互交流，并与该领域的领导者，并将帮助他们理解的主要问题，并学习该领域的前沿方法。概率和偏微分方程一直交织在一起，现代研究继续进一步interleaving他们。一个共同的方面是如何将随机性引入偏微分方程，例如随机初始数据，随机环境，随机强迫将深刻影响长期行为，因为它提供了一个灵活和现实的方法来研究物理模型，或者因为它是基础系统模型的一个不可避免的特征。另一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中的多主体问题。该计划将汇集世界各地的专家和初级研究人员在一个密集和集中的计划，这将有助于大大进一步了解这些现象，这个奖项将有助于培养这些方法的下一代美国科学家。专题学期网站在http://www.crm.umontreal.ca/2022/Probab22/index_e.php维护，分支系统，反应扩散方程和人口模型研讨会在http://www.crm.umontreal.ca/2022/Systemes22/index_e.php和随机性统一概念的PDE研讨会在http://www.crm.umontreal.ca/2022/Concepts22/index_e.php.This奖反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.