Interacting Particle Systems and Mean-field games Workshops

交互粒子系统和平均场游戏研讨会

• 批准号: 2207572
• 负责人: Kavita Ramanan
• 金额: $ 2.5万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-02-15 至 2023-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2207572&HistoricalAwards=false
• 关键词: Interacting; Particle; Systems; Mean; field

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.

该项目将支持研究生，博士后研究人员和来自美利坚合众国的早期职业研究人员参加的一个研讨会之一，将于3月13日至27日，2022年3月13日至27日将于2022年4月10日至17日在2022年4月10日至17日在De Recherches Matherematequique shorematique crm crm crm crm crm crm crm crm horm inshop举行。这两个研讨会都是从2022年1月至7月在CRM举行的有关“概率和PDE”的较大跨学科主题计划的一部分。概率理论和部分微分方程（PDES）是数学的重要领域，其方法和目标是实质性重叠的。在这两个领域中，主要目的之一是提供准确的模型，以随着时间的流逝而设计，物理，化学和生物系统如何变化。概率通常集中在微观水平上如何随机和/或不可预测的系统如何在宏观级别上升。 PDE理论经常着重于此类宏观系统的空间和临时演变。几十年来，两个字段的概率和PDE之间一直存在着富有成果的相互作用，以及每个区域发现应用程序中的直觉和数学技术。该项目的重点是该相互作用的两个方面，这两者都与概率粒子系统非常类似于PDE时，这两个方面都非常“放大”。其中之一是平均场游戏的区域，描述了策略控制的相互作用代理的缩放限制，因为差异是通过图形结构（通常是完整的图）结合的。第二个相互作用的粒子系统和流体动力限制通常集中于更几何设置（例如晶格）中粒子系统的PDE近似（在时空和时间上都有适当的细网限制）。 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奖反映了NSF的法定任务，并被认为是通过基金会的知识分子优点和更广泛影响的评估来评估的审查标准。