RTG: Research Training in Applied Mathematics at Columbia University

RTG：哥伦比亚大学应用数学研究培训

• 批准号: 1937254
• 负责人: Kui Ren
• 金额: $ 191.32万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-08-01 至 2025-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1937254&HistoricalAwards=false
• 关键词: RTG; Research; Training; Applied; Mathematics

This Research Training Group (RTG) project is a joint effort of the Department of Applied Physics and Applied Mathematics, the Department of Mathematics, and the School of Engineering and Applied Sciences at Columbia University. It aims to create a cutting-edge research and training program in modern applied mathematics. By substantially enriching research and educational experiences for trainees, and by directly coupling into key educational and research initiatives in the School of Engineering and Applied Sciences and across the University, the activities will have a significant impact on applied mathematics education and training at Columbia. The RTG project will engage high school as well as undergraduate students from the New York metropolitan area and across the country (through the Summer Research Program), inspiring mathematical careers for underrepresented groups in the United States.The project includes three main ingredients: (i) a group of research topics in applied mathematics at the frontier of engineering applications; (ii) a coherent mentoring-learning program on applied mathematics research and career development for undergraduate and graduate students as well as postdoctoral scholars; and (iii) a systematic plan to modernize undergraduate and graduate curriculum in applied mathematics and scientific computation. The senior investigators and the trainees will form groups to tackle challenging and rewarding mathematical and computational problems, including linear and nonlinear wave propagation in novel complex (and possibly random) structures, physics- and data-enabled algorithms for material discovery, hybrid inverse problems and imaging, mathematical theory of machine learning, harmonic analysis of large data sets, and uncertainty quantification. They will collaborate with leading engineers at Columbia to connect their mathematical and computational discoveries with applications in nonlinear optics and photonics, materials science, medical imaging, climate modeling, and general data science. The senior members of this RTG project are strongly committed to training and mentoring undergraduates, graduate students, and postdoctoral scholars. Their extensive and varied experiences in teaching and mentorship will be invaluable to the professional growth of the trainees.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.

该研究培训小组（RTG）项目是应用物理和应用数学系，数学系以及哥伦比亚大学工程和应用科学学院的共同努力。它旨在在现代应用数学中创建尖端的研究和培训计划。通过实质上丰富了学员的研究和教育经验，并直接与工程和应用科学学院以及整个大学的关键教育和研究计划结合在一起，这些活动将对哥伦比亚的应用数学教育和培训产生重大影响。 RTG项目将吸引高中以及来自纽约大都会地区和全国各地（通过夏季研究计划）的高中以及本科生，激发了美国代表性不足的群体的数学职业。 （ii）针对本科生和研究生以及博士后学者的应用数学研究和职业发展的连贯指导学习计划； （iii）在应用数学和科学计算中现代化本科和研究生课程的系统计划。高级研究人员和学员将组建小组，以解决具有挑战性的数学和计算问题，包括新颖的复杂（可能是随机）结构的线性和非线性波传播，物理和数据支持的算法，用于物质发现，混合逆问题，杂交问题，成像，数学理论，机器学习的数学理论，机器学习，无限数据设置和无数据分析，并确定了确定度量。他们将与哥伦比亚的领先工程师合作，将其数学和计算发现与非线性光学和光子学，材料科学，医学成像，气候建模和一般数据科学的应用联系起来。该RTG项目的高级成员强烈致力于培训和指导本科生，研究生和博士后学者。他们在教学和指导方面的广泛经验将对受训者的专业成长非常宝贵。该奖项反映了NSF的法定使命，并且使用基金会的知识分子优点和更广泛的影响审查标准，被认为值得通过评估来获得支持。

项目成果

The ASEP speed process

ASEP 速度流程

• DOI: 10.1016/j.aim.2023.109004
• 发表时间: 2023
• 期刊: Advances in Mathematics
• 影响因子: 1.7
• 作者: Aggarwal, Amol;Corwin, Ivan;Ghosal, Promit
• 通讯作者: Ghosal, Promit

Francis Comets’ Gumbel last passage percolation

弗朗西斯·科梅茨 (Francis Comet) 甘贝尔最后一段渗透

• DOI: 10.1016/j.spa.2023.104267
• 发表时间: 2024
• 期刊: Stochastic Processes and their Applications
• 影响因子: 1.4
• 作者: Corwin, Ivan

Spatial Tightness at the Edge of Gibbsian Line Ensembles

吉布斯线系综边缘的空间紧密性

• DOI: 10.1007/s00220-022-04509-4
• 发表时间: 2023
• 期刊: Communications in Mathematical Physics
• 影响因子: 2.4
• 作者: Barraquand, Guillaume;Corwin, Ivan;Dimitrov, Evgeni
• 通讯作者: Dimitrov, Evgeni

Stationary measures for the log-gamma polymer and KPZ equation in half-space

• DOI: 10.1214/23-aop1634
• 发表时间: 2022-03
• 期刊: The Annals of Probability
• 作者: Guillaume Barraquand;Ivan Corwin

A space-time nonlocal traffic flow model: Relaxation representation and local limit

时空非局部交通流模型：松弛表示和局部极限

• DOI: 10.3934/dcds.2023054
• 发表时间: 2023
• 期刊: Discrete and Continuous Dynamical Systems
• 影响因子: 1.1
• 作者: Du, Qiang;Huang, Kuang;Scott, James;Shen, Wen
• 通讯作者: Shen, Wen