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 3 月 13 日至 27 日举行的“相互作用粒子系统和流体动力学极限”研讨会之一，或“平均场游戏”研讨会将于 2022 年 4 月 10 日至 17 日在加拿大蒙特利尔数学研究中心 (CRM) 举行。这两个研讨会都是更大的跨学科研讨会的一部分2022 年 1 月至 7 月在 CRM 举办的“概率与偏微分方程”主题课程。概率论和偏微分方程 (PDE) 理论是数学的重要领域，在这两个领域中，它们的方法和目标有很大的重叠。概率论的主要目标是提供工程、物理、化学和生物系统如何随时间变化的准确模型，概率论经常关注微观层面上随机和/或不可预测的系统如何在宏观层面上变得高度有序。几十年来，概率论和偏微分方程这两个领域之间的相互作用经常集中在宏观系统的空间和时间演化上，每个领域的直觉和数学技术都在另一个领域得到了应用。这种相互作用的各个方面，都与概率粒子系统在充分“缩小”时如何类似于偏微分方程有关，其中之一是平均场博弈的区域，描述了策略控制的相互作用主体随着扩散耦合而演化的尺度限制。图结构（通常是完整的图）。第二个相互作用的粒子系统和流体动力学极限通常侧重于更多几何设置中的粒子系统的 PDE 近似，例如晶格（在空间和时间目标上采用适当的细网格极限）。该项目的目的是支持美国的初级研究人员和来自代表性不足群体的研究人员参与关于概率和偏微分方程的主题学期（特别是他们参加关于平均场博弈和相互作用粒子主题的两个研讨会）系统），将于 2022 年上半年在加拿大蒙特利尔数学研究中心举行。该学期的主题网站位于 http://www.crm.umontreal.ca/2022/Probab22/index_e.php。粒子系统和流体动力学极限研讨会，网址：http://www.crm.umontreal.ca/2022/Particules22/index_e.php 和平均场游戏研讨会，网址：http://www.crm.umontreal.ca/2022/Games22/index_e.php。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查进行评估，被认为值得支持标准。