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）项目是哥伦比亚大学应用物理与应用数学系、数学系和工程与应用科学学院的共同努力。它旨在创建现代应用数学的前沿研究和培训计划。通过大大丰富研究和培训学员的教育经验，并直接耦合到工程和应用科学学院和整个大学的关键教育和研究举措，这些活动将对应用数学教育和培训产生重大影响哥伦比亚。RTG项目将吸引来自纽约大都会地区和全国各地的高中生和本科生（通过暑期研究计划），为美国未被充分代表的群体提供数学职业激励。该项目包括三个主要组成部分：（i）一组工程应用前沿的应用数学研究课题;（ii）为本科生、研究生和博士后学者提供有关应用数学研究和职业发展的连贯导学计划;及（iii）有系统地推行计划，使本科生和研究生的应用数学和科学计算课程现代化。高级研究人员和学员将组成小组，解决具有挑战性和有益的数学和计算问题，包括新型复杂（可能是随机）结构中的线性和非线性波传播，材料发现的物理和数据支持算法，混合逆问题和成像，机器学习的数学理论，大型数据集的谐波分析，以及不确定性量化。他们将与哥伦比亚的顶尖工程师合作，将他们的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、气候建模和通用数据科学的应用联系起来。这个RTG项目的高级成员坚定地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而多样的经验对学员的专业成长将是无价的。这个奖项反映了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标准进行评估，被认为值得支持。

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

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

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

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