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.

该研究培训小组专注于动力系统接口、概率论和偏微分方程。该项目为本科生、研究生和博士后参与者提供培训机会，旨在促进博士后研究员和教师的创造力、领导力和专业发展。该项目包括向当地 K-12 学校进行推广；本科生在学年和暑期的研究经验，包括与为许多来自数学科学领域代表性不足的群体的学生提供服务的机构的教师合作；研究生和博士后暑期学校；和交流研讨会。该项目特别强调沟通，这既是因为它对于接触更广泛的公众的重要性，也是因为它在数学本身中的重要作用。由于概率、动力学和偏微分方程跨越了纯数学和应用数学之间经常存在的鸿沟，因此这些科目为有效沟通提供了极好的训练基础。动力系统、概率论和偏微分方程具有丰富的相互联系，涵盖了从理论到应用的整个数学活动范围。然而，在本科生或研究生教育中很少探讨这种相互联系。该项目旨在强调这些联系，这些联系已被证明在研究前沿卓有成效，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相关的问题。对沟通的重视将促进参与者的专业发展，无论他们从事教育、工业还是研究工作。本科生的暑期学校和研究经历将吸引全国范围内符合条件的参与者。作为推广和建模活动一部分创建的教育模块将在线向学校、大学和公众开放。外展活动将邀请高中生加入数学发现的兴奋之中，同时为研究生提供担任导师的机会。

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）

Optimal Path-Planning With Random Breakdowns

随机故障的最优路径规划

DOI：
10.1109/lcsys.2021.3130193
发表时间：
2022-01
期刊：
IEEE Control Systems Letters
影响因子：
3
作者：
Gee, Marissa;Vladimirsky, Alexander
通讯作者：
Vladimirsky, Alexander

Designing Robust Networks of Coupled Phase Oscillators With Applications to the High Voltage Electric Grid

设计鲁棒的耦合相位振荡器网络及其在高压电网中的应用

DOI：
10.1109/tcns.2022.3214778
发表时间：
2022-01-04
期刊：
IEEE Transactions on Control of Network Systems
影响因子：
4.2
作者：
Shriya V. Nagpal;G. G. Nair;F. Parise;C. L. Anderson
通讯作者：
C. L. Anderson

Concentration for integrable directed polymer models

可积定向聚合物模型的浓度

DOI：
10.1214/21-aihp1154
发表时间：
2022-02
期刊：
Probabilités et Statistiques
影响因子：
0
作者：
Noack, Christian;Sosoe, Philippe
通讯作者：
Sosoe, Philippe

Anisotropic challenges in pedestrian flow modeling

行人流建模中的各向异性挑战

DOI：
10.4310/cms.2018.v16.n4.a7
发表时间：
2018-01
期刊：
Communications in Mathematical Sciences
影响因子：
1
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：
2019-08
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