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.

该研究培训小组着重于动态系统，概率理论和部分微分方程的界面。该项目为本科，毕业生和博士后参与者提供了培训机会，并旨在进一步发展博士后研究员和教师的创造力，领导和专业发展。该项目包括向当地K-12学校推广；在学年和夏季，本科生的研究经验，包括与机构的伙伴关系，这些机构为许多数学科学人数不足的团体的学生提供服务；研究生和博士后研究员的暑期学校；和沟通研讨会。该计划特别强调沟通，这既是因为它在吸引更广泛的公众方面的重要性，又是其在数学本身中的重要作用。由于概率，动力学和部分微分方程跨越了通常存在于纯数学和应用数学之间的鸿沟，因此这些主题为有效的交流提供了良好的训练场。动力学系统，概率理论和部分微分方程具有丰富的互连，并跨越了从理论到应用的整个数学活动。但是，在本科或研究生教育中很少探索这种互连。该项目旨在强调这些联系，这些联系在研究边界已被证明是如此富有成果，从而扩大了下一代数学家的观点。研究活动将向学生介绍与社会和环境问题有关的问题。对沟通的强调将增强参与者的专业发展，无论他们发现自己从事教育，工业还是研究工作。本科生的暑期学校和研究经验将吸引全国合格的参与者。作为推广和建模活动的一部分创建的教育模块将在学校，大学和公众在线提供。外展活动将邀请高中生加入数学发现的兴奋，同时给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

Concentration for integrable directed polymer models

可积定向聚合物模型的浓度