Research in Mathematics

数学研究

基本信息

批准号：
1638352
负责人：
Helmut Hofer
金额：
$ 799.88万
依托单位：
Institute For Advanced Study
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-09-01 至 2021-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1638352&HistoricalAwards=false
关键词：
Research Mathematics

项目摘要

The School of Mathematics (SoM) at the Institute for Advanced Study (IAS) has two primary goals. First, it supports fundamental research in mathematics, encourages original thinking, and produces significant advances in knowledge. Second, it invests in the development of a diverse pool of mathematical talent. The School strongly encourages the participation of women and members of other groups underrepresented in mathematics, and is dedicated to furthering the education and careers of all of its postdoctoral fellows. Junior mathematicians benefit from both their interactions with senior scholars and the mentoring they receive from faculty members. Mid-career and senior mathematicians consolidate their research projects and explore new research directions. The School's emphasis on a unified, interdisciplinary mathematical perspective and its work in bringing together a diverse group of mathematicians has led to numerous unanticipated mathematical developments. The School is in a strong position to identify, at an early stage, subject areas with the potential for important new developments. The School is led by eight permanent faculty members whose expertise span a wide spectrum of mathematics. As a center for new collaborations and new lines of research, the School hosts approximately 75 visiting mathematicians annually whose collaborative research visits typically last 4-10 months. This grant supports 23 of these scholars (17 postdoctoral fellows and 6 mid-career mathematicians), who join approximately 50 other mathematicians supported by funds from other sources. It also provides funds to host small groups of collaborators during the summer.The School of Mathematics provides this diverse community of scholars with an interactive environment, rich in mathematical content and conducive to collaboration. Each year SoM conducts a special program focused on a particularly exciting field of mathematics. The programs for the next three years will be "Locally Symmetric Spaces: Analytical and Topological Aspects" in 2017-2018; "Variational Methods in Geometry" in 2018-2019; and "Optimization, Statistics, and Theoretical Machine Learning" in 2019-2020. Each semester SoM facilitates a week-long workshop associated with the special topical program, as well as a separate week-long working group. The "Emerging Topics Working Group" is a group of researchers selected to work on a topic which seems ripe for significant progress. Other programs include "Mathematical Conversations," an informal discussion group that meets once a week, and "Summer Collaborators," small groups of invited researchers who collaborate on special research projects during the summer months. In addition to these workshops and programs, the SoM offers regular seminars, lecture series, and reading groups. All IAS lectures are videotaped and are available to the public. Visiting mathematicians supported by the grant receive individual and group mentoring from the permanent faculty members. Their individual research projects dive into one or more of the following fields of study: Analysis, Partial Differential Equations of Applied Mathematics, Probability, Algebra, Algebraic Geometry, Lie Groups, Representation Theory, Differential Geometry, Topology, Mathematical Physics, Dynamical Systems, Computer Science, Discrete Mathematics, Theoretical Machine Learning, and Number Theory.

高级研究研究所（IAS）的数学学院（SOM）有两个主要目标。首先，它支持数学方面的基本研究，鼓励原始思维，并在知识方面产生重大进展。其次，它投资于多种数学人才库的发展。学校强烈鼓励妇女的参与和其他人为数学缺乏的团体的参与，并致力于促进所有博士后研究员的教育和职业。初级数学家从与高级学者的互动及其从教职员工那里获得的指导中受益。职业生涯和高级数学家巩固了他们的研究项目，并探索了新的研究指示。学校的重点是统一的跨学科数学观点及其在汇集一群数学家群体方面的工作，导致了许多意外的数学发展。该学校在早期阶段就处于强大的位置，具有重要的新发展的主题领域。这所学校由八名常任教师领导，他们的专业知识涵盖了广泛的数学。作为新的合作中心和新的研究线中心，该学校每年约有75名访问数学家，他们的合作研究访问通常持续4-10个月。这项赠款支持了其中23名学者（17名博士后研究员和6位职业中学数学家），他们加入了大约50位其他数学家，并得到了其他来源的资金支持。它还提供了资金，可以在夏季接待小组合作者。数学学院为这个多样化的学者社区提供了互动环境，富含数学内容，并有利于协作。每年，SOM都会进行一项特别的计划，重点是一个特别令人兴奋的数学领域。未来三年的计划将在2017 - 2018年为“本地对称空间：分析和拓扑方面”； 2018 - 2019年的“几何方法的变异方法”；以及2019 - 2020年的“优化，统计和理论机器学习”。每个学期的SOM促进了与特殊主题计划相关的为期一周的研讨会以及一个单独的一周工作组。 “新兴主题工作组”是一组研究人员，他们被选为研究主题，这似乎是成熟的，以取得重大进展。其他计划包括“数学对话”，一个非正式的讨论小组，每周开会一次，以及“夏季合作者”，这是一小部分邀请的研究人员，他们在夏季进行了特殊研究项目。除了这些研讨会和计划外，SOM还提供定期的研讨会，讲座系列和阅读小组。所有IAS讲座均录像，可向公众使用。赠款支持的来访数学家会从永久教师那里获得个人和团体指导。他们的个人研究项目涉足以下一个或多个研究领域：分析，应用数学的部分微分方程，概率，代数，代数几何，谎言组，代表理论，差异几何，拓扑，数学，数学物理学，动态系统，计算机科学，计算机科学，学位数学，数学，理学的机器学习和数字理论。