RTG Analysis

RTG分析

• 批准号: 1344970
• 负责人: Mario Bonk
• 金额: $ 200万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-07-01 至 2020-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1344970&HistoricalAwards=false
• 关键词: RTG; Analysis

The goal of this project is to increase the number of US citizens and permanent residents who are able to employ advanced mathematical ideas for independent research or applications in other fields. The major emphasis of the project will be the education of graduate students who want to obtain a PhD in mathematics, and the promotion of the careers of postdoctoral researchers who are affiliated with the analysis group at the University of California, Los Angeles. A variety of measures involving members of the analysis group is intended to attract students on all levels to mathematics and possibly to the area of analysis. The goal is to secure a "pipeline" of suitable candidates who want to learn advanced mathematical concepts and help them to be successful with this quest. For elementary, middle, and high school students these initiatives include the cooperation with the Los Angeles Math Circle that has regular meetings on Sundays and offers expository lectures, problem-solving sessions, and study groups. For undergraduates there will be summer review sessions with a view towards preparation for the GRE subject test in mathematics. Incoming graduate students will benefit from the "Boot Camp", an intensive six-week long review session on central topics in mathematics that is intended to facilitate the transition between undergraduate and graduate training. These additional activities will be "vertically integrated" to ensure interactions between students and researchers on all levels with a twofold goal in mind: improving the communication and presentation skills of the research trainees and raising the awareness of students, in particular among underrepresented groups, for mathematics as an interesting and exciting field of study.Since the times of Leibniz and Newton, analysis has been one of the core subjects of mathematics. It has led to many spectacular applications in science and engineering. By now analytic tools are ubiquitous in all areas of investigation based on quantitative reasoning. Many of the more prominent recent advances within mathematics itself rely heavily on sophisticated analytic methods. Examples are Perelman's solution of Thurston's geometrization conjecture for 3-manifolds, the work by Lawler-Schramm-Werner on the stochastic Loewner equation and its applications for random processes, or the investigations by Tao-Vu on universality laws in random matrix theory. Today analysis is a vibrant area of mathematical investigation with a wide range of applications. The analysis group in the Department of Mathematics at UCLA includes many distinguished researchers and has a high standing in comparative rankings. Its members have a broad range of research interests including operator algebras, partial differential equations, complex analysis, harmonic analysis, mathematical physics, probability, and analytic number theory. In addition to the strength of its researchers, the analysis group has a long and successful history of training mathematicians. With the diversity of interests within the group and its strong past record, it has the unique expertise to impart a broad vision of the field to its students and to train the next generation of experts in analysis.

该项目的目标是增加美国公民和永久居民的数量，他们能够将先进的数学思想用于其他领域的独立研究或应用。该项目的主要重点将是希望获得数学博士学位的研究生的教育，以及促进隶属于洛杉矶加州大学分析小组的博士后研究人员的职业发展。 涉及分析小组成员的各种措施旨在吸引各级学生学习数学，并可能学习分析领域。我们的目标是确保一个“管道”的合适的候选人谁想要学习先进的数学概念，并帮助他们成功地与这个追求。 对于小学、初中和高中学生，这些举措包括与洛杉矶数学圈合作，该数学圈在周日定期开会，并提供临时讲座、解决问题的会议和学习小组。对于本科生，将有夏季复习课程，以准备GRE数学科目考试。 即将到来的研究生将受益于“靴子营”，一个密集的为期六周的审查会议的中心议题的数学，旨在促进本科和研究生培训之间的过渡。 这些额外的活动将是“纵向一体化”，以确保学生和研究人员之间的互动在所有层面上考虑到双重目标：提高研究学员的沟通和表达技能，提高学生的认识，特别是在代表性不足的群体中，数学是一个有趣和令人兴奋的研究领域。自莱布尼茨和牛顿时代以来，分析一直是数学的核心学科之一。它在科学和工程领域有许多惊人的应用。到目前为止，分析工具在基于定量推理的所有调查领域中无处不在。数学本身的许多更突出的最新进展在很大程度上依赖于复杂的分析方法。例子是佩雷尔曼的解决方案瑟斯顿的geometriization猜想为3流形，工作的劳勒，施拉姆-沃纳的随机Loewner方程及其应用的随机过程，或调查的陶武的普遍性法律在随机矩阵理论。今天的分析是一个充满活力的领域的数学调查与广泛的应用。加州大学洛杉矶分校数学系的分析小组包括许多杰出的研究人员，在比较排名中具有很高的地位。其成员有广泛的研究兴趣，包括算子代数，偏微分方程，复分析，调和分析，数学物理，概率和解析数论。除了其研究人员的实力，分析组有一个长期和成功的历史，培养数学家。凭借集团内部的利益多样性和强大的过去记录，它拥有独特的专业知识，可以向学生传授该领域的广阔视野，并培养下一代分析专家。