Mathematical Sciences Research Institute (MSRI)

点击翻译按钮获取中文摘要

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.