Mathematical Sciences Research Institute (MSRI)

数学科学研究所（MSRI）

基本信息

批准号：
1928930
负责人：
Tatiana Toro
金额：
$ 2500万
依托单位：
Mathematical Sciences Research Institute
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：
2020-09-01 至 2025-08-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1928930&HistoricalAwards=false
关键词：
Mathematical Sciences Research Institute MSRI

项目摘要

Mathematical sciences research is key to progress in many areas of technology, healthcare, and national security. The Mathematical Sciences Research Institute (MSRI) in Berkeley, California strengthens U.S. research in the mathematical sciences through innovative and intensive semester-long programs and workshops as well as through the training of postdoctoral fellows and graduate students. In addition, MSRI contributes to public education and enhances the appreciation of mathematics through public events and widely distributed videos. In all of its activities, MSRI strives to be a model of innovation and best practices in encouraging inclusivity. The Institute has long been recognized as a world center of collaborative mathematics research and it will continue to expand its national impact by exploring new research areas and creating new collaborations. MSRI's programs bring together both early-career and established mathematical scientists from a wide range of institutions. In these programs, postdoctoral fellows and graduate students meet the subject's leaders, as well as some of their most creative future colleagues, providing a powerful influence on their scientific development and future careers. MSRI's Summer Graduate Schools enrich PhD students with collaborative experiences around new subjects often outside of the standard curriculum. The Institute's nationally visible programs, such as Numberphile and the National Math Festival, improve the public appreciation of mathematics and its importance to society, while the annual Critical Issues in Mathematics Education Workshops connect mathematicians and math educators. MSRI's programs range over the spectrum of fundamental mathematics. Each program brings together a group of specialists, including those interested in applications, and for that time MSRI becomes a global center of activity in the program's subject. Postdoctoral fellows and advanced graduate students add to the intellectual excitement and influence of the programs, and they find an environment for research beyond what they had in graduate school. The Institute combines fields and pairs programs in ways that lead to new connections and sometimes catalyze the recognition of a new field. In 2022, the program on Analytic and Geometric Aspects of Gauge Theory will be paired with one on Floer Homotopy, which has the potential to deeply enrich both fields. The development of Floer theory can be seen as a parallel to the emergence of algebraic topology in the first half of the 20th century, going from counting invariants to homology groups, and beyond that to the construction of algebraic structures on these homology groups and their underlying chain complexes. The goal of this program is to relate these developments to Floer theory with the dual aims of (1) better understanding symplectic and low-dimensional topology, and (2) providing a new set of geometrically motivated questions in homotopy theory. MSRI can also respond quickly to new developments through its Hot Topics Workshops. In 2020, MSRI will host a workshop on Optimal Transport and Applications to Machine Learning and Statistics. The workshop will explore the many emerging connections between the theory of Optimal Transport and models and algorithms currently used in the Machine Learning community. Some programs treat more applied subjects, such as the 2021 programs on Fluid Dynamics and Universality and Integrability in Random Matrix Theory and Interacting Particle Systems. The past decade has seen tremendous progress in understanding the behavior of large random matrices and interacting particle systems. Complementary methods have emerged to prove universality of these behaviors, as well as to probe their precise nature using integrable, or exactly solvable models.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.

数学科学研究是许多技术，医疗保健和国家安全领域进步的关键。加利福尼亚州伯克利的数学科学研究所（MSRI）通过创新的，密集的学期课程和讲习班以及对博士后研究员和研究生的培训，通过创新和强化的学期课程和研讨会来增强美国在数学科学方面的研究。此外，MSRI通过公共事件和广泛分布的视频为公共教育做出了贡献，并增强了数学的欣赏。在所有活动中，MSRI致力于成为鼓励包容性的创新和最佳实践模式。该研究所长期以来一直被公认为是合作数学研究的世界中心，它将继续通过探索新的研究领域并创建新的合作来扩大其国家影响。 MSRI的计划汇集了来自各种机构的早期职业和建立数学科学家。在这些计划中，博士后研究员和研究生与受试者的领导者以及他们一些最具创造力的未来同事会面，从而对他们的科学发展和未来的职业产生了强大的影响。 MSRI的暑期研究生院丰富了博士生，并在标准课程之外围绕新科目的合作经验丰富了合作经验。该研究所的全国可见计划，例如数字和国家数学节，提高了对数学及其对社会重要性的公众欣赏，而数学教育研讨会上的年度关键问题将数学家和数学教育者联系起来。 MSRI的计划范围范围为基本数学的范围。每个计划都汇集了一组专家，包括对应用程序感兴趣的专家，而在此期间，MSRI成为该计划主题的全球活动中心。博士后研究员和高级研究生增加了计划的智力兴奋和影响力，他们为研究生院的研究环境找到了一个研究环境。该研究所以导致新联系的方式结合了领域和对计划，有时会催化对新领域的认可。在2022年，仪表理论的分析和几何方面计划将与浮子同质性配对，该程序有可能深入富集这两个领域。浮子理论的发展可以看作是20世纪上半叶代数拓扑的出现，从计数不变到同源性群体，再到这些同源性组及其基础链复合物的代数结构的构建。该计划的目的是将这些发展与浮动理论联系起来，以（1）更好地理解符号和低维拓扑的双重目的，以及（2）在同义理论中提供一组新的几何动机问题。 MSRI还可以通过其热门话题研讨会快速回应新的发展。在2020年，MSRI将举办一个关于机器学习和统计信息的最佳运输和应用的研讨会。该研讨会将探讨机器学习社区当前使用的最佳运输理论与最佳传输理论和算法之间的许多新兴联系。一些程序处理更多应用的主题，例如随机矩阵理论和相互作用的粒子系统中有关流体动力学以及普遍性的2021个程序。过去十年在理解大型随机矩阵和相互作用粒子系统的行为方面取得了巨大进展。已经出现了互补的方法来证明这些行为的普遍性，并使用可解决的模型或可解决的模型来探究其精确的性质。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的审查标准通过评估来进行评估的。