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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.

数学科学研究是技术，医疗保健和国家安全许多领域进步的关键。位于加州伯克利的数学科学研究所（MSRI）通过创新和密集的学期课程和研讨会以及博士后研究员和研究生的培训加强了美国在数学科学方面的研究。此外，MSRI还通过公共活动和广泛分发的视频为公共教育做出了贡献，并提高了对数学的认识。在其所有活动中，MSRI努力成为鼓励包容性的创新和最佳做法的典范。该研究所长期以来一直被公认为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和创造新的合作来扩大其国家影响力。MSRI的项目汇集了来自众多机构的早期职业生涯和成熟的数学科学家。在这些项目中，博士后研究员和研究生会见了该学科的领导者，以及他们未来最具创造力的同事，对他们的科学发展和未来的职业生涯产生了强大的影响。MSRI的暑期研究生院丰富了博士生的合作经验，围绕新的主题，往往在标准课程之外。该研究所的全国可见的计划，如Numberphile和国家数学节，提高了公众对数学及其对社会的重要性的认识，而每年的数学教育研讨会的关键问题连接数学家和数学教育工作者。MSRI的课程涵盖基础数学的各个领域。每个项目都汇集了一组专家，包括那些对应用感兴趣的人，那时MSRI成为该项目主题的全球活动中心。博士后研究员和高级研究生增加了知识的兴奋和程序的影响力，他们发现一个研究环境超出了他们在研究生院。该研究所结合领域和配对方案的方式，导致新的连接，有时催化一个新领域的认可。在2022年，规范理论的分析和几何方面的计划将与Floer同伦配对，这有可能大大丰富这两个领域。弗洛尔理论的发展可以被看作是一个平行的出现代数拓扑学在上半个世纪，从计数不变量的同源群，并超越了建设的代数结构对这些同源群和他们的基础链复合体。本计划的目标是将这些发展与Floer理论联系起来，其双重目标是（1）更好地理解辛和低维拓扑，以及（2）提供一组新的同伦理论中的几何动机问题。MSRI还可以通过其热点专题研讨会快速响应新的发展。在2020年，MSRI将举办一个关于最佳运输和机器学习和统计应用的研讨会。研讨会将探讨最优传输理论与机器学习社区目前使用的模型和算法之间的许多新兴联系。一些程序处理更多的应用主题，如2021年的程序在流体动力学和普遍性和可积性随机矩阵理论和相互作用的粒子系统。在过去的十年里，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的进展。补充方法已经出现，以证明这些行为的普遍性，以及探测其精确的性质，使用可积，或完全可解的models.This award reflects NSF的法定使命，并已被认为是值得的支持，通过评估使用基金会的智力价值和更广泛的影响审查标准.

项目成果

期刊论文数量（92）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

On the Rouquier dimension of wrapped Fukaya categories and a conjecture of Orlov

DOI：
10.1112/s0010437x22007886
发表时间：
2021-10
期刊：
Compositio Mathematica
影响因子：
1.8
作者：
Shaoyun Bai;Laurent Cot'e
通讯作者：
Shaoyun Bai;Laurent Cot'e

Toward Achieving a Vaccine-Derived Herd Immunity Threshold for COVID-19 in the U.S.

在美国获得疫苗来源的疫苗豁免阈值

DOI：
10.3389/fpubh.2021.709369
发表时间：
2021
期刊：
Frontiers in public health
影响因子：
5.2
作者：
Gumel AB;Iboi EA;Ngonghala CN;Ngwa GA
通讯作者：
Ngwa GA

K-homology and K-theory for pure braid groups

纯辫群的 K 同调和 K 理论

DOI：
发表时间：
2022
期刊：
New York journal of mathematics
影响因子：
0.6
作者：
Azzali, Sara;Browne, Sarah L.;Gomez Aparicio, Maria Paula;Ruth, Lauren C.;Wang, Hang
通讯作者：
Wang, Hang

Existence results for fractional order functional differential equations with infinite delay in the sense of the deformable derivative

变形导数意义上无限时滞分数阶泛函微分方程的存在性结果