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RTG: Dynamics, Probability, and Partial Differential Equations in Pure and Applied Mathematics

RTG：纯粹数学和应用数学中的动力学、概率和偏微分方程

基本信息

批准号：
1645643
负责人：
Steven Strogatz
金额：
$ 249.45万
依托单位：
Cornell University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-09-01 至 2024-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1645643&HistoricalAwards=false
关键词：
RTG Dynamics Probability Partial Differential

项目摘要

This research training group focuses on the interface of dynamical systems, probability theory, and partial differential equations. The project provides training opportunities for undergraduate, graduate, and postdoctoral participants and aims to further the creativity, leadership, and professional development of postdoctoral fellows and faculty. The project includes outreach to local K-12 schools; research experiences for undergraduates, both during the academic year and summer, including partnerships with faculty at institutions that serve many students from groups underrepresented in the mathematical sciences; summer schools for graduate students and postdoctoral fellows; and a communication seminar. The program especially emphasizes communication, both because of its importance in reaching the wider public, and for its vital role within mathematics itself. Because probability, dynamics, and partial differential equations straddle the divide that often exists between pure and applied mathematics, these subjects provide an excellent training ground for effective communication. Dynamical systems, probability theory, and partial differential equations have rich interconnections and span the entire spectrum of mathematical activities from theory to applications. However, such interconnections are rarely explored in undergraduate or graduate education. This project aims to highlight these connections, which have proven so fruitful at the research frontier, and thereby to broaden the perspective of the next generation of mathematicians. The research activities will introduce students to problems relevant to societal and environmental issues. The emphasis on communication will enhance the professional development of participants, whether they find themselves working in education, industry, or research. The summer schools and research experiences for undergraduates will attract eligible participants nationwide. The educational modules created as part of the outreach and modeling activities will be available online to schools, universities, and the general public. The outreach activities will invite high school students to join in the excitement of mathematical discovery, while giving graduate students an opportunity to act as mentors.

这个研究训练小组的重点是动力系统，概率论和偏微分方程的接口。该项目为本科生，研究生和博士后参与者提供培训机会，旨在进一步提高博士后研究员和教师的创造力，领导力和专业发展。该项目包括与当地K-12学校的外联活动;在学年和夏季为本科生提供研究经验，包括与为数学科学代表性不足的群体的许多学生提供服务的机构的教师建立伙伴关系;为研究生和博士后研究员开设暑期学校;以及一个交流研讨会。该计划特别强调沟通，因为它在接触更广泛的公众的重要性，并在数学本身的重要作用。因为概率论、动力学和偏微分方程跨越了纯数学和应用数学之间的鸿沟，这些学科为有效的交流提供了一个很好的训练基地。动力系统、概率论和偏微分方程之间有着丰富的相互联系，它们跨越了从理论到应用的整个数学活动范围。然而，这种相互联系很少在本科或研究生教育中探讨。该项目旨在突出这些联系，这些联系在研究前沿已被证明是如此富有成效，从而拓宽下一代数学家的视野。研究活动将向学生介绍与社会和环境问题有关的问题。对沟通的重视将加强参与者的专业发展，无论他们是在教育，工业还是研究领域工作。本科生暑期学校和研究经验将吸引全国符合条件的参与者。作为推广和建模活动的一部分创建的教育模块将在网上提供给学校，大学和公众。外展活动将邀请高中生加入数学发现的兴奋，同时让研究生有机会担任导师。

项目成果

期刊论文数量（33）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Control-Theoretic Models of Environmental Crime

环境犯罪的控制理论模型

DOI：
10.1137/19m1270483
发表时间：
2020
期刊：
SIAM Journal on Applied Mathematics
影响因子：
1.9
作者：
Cartee, Elliot;Vladimirsky, Alexander
通讯作者：
Vladimirsky, Alexander

Epidemic threshold and lifetime distribution for information diffusion on simultaneously growing networks

同时增长的网络上信息传播的流行病阈值和生命周期分布

DOI：
10.1145/3341161.3342891
发表时间：
2019
期刊：
ASONAM '19: Proceedings of the 2019 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining
影响因子：
0
作者：
Fischer, Emily M.;Ghosh, Souvik;Samorodnitsky, Gennady
通讯作者：
Samorodnitsky, Gennady

Continuous Analogues of Krylov Subspace Methods for Differential Operators

微分算子的 Krylov 子空间方法的连续类似