Research in Mathematics

高等研究院(IAS)数学学院(SOM)有两个主要目标。首先，它支持数学基础研究，鼓励原创思维，并在知识方面产生重大进步。其次，它投资于培养多样化的数学人才。该学院大力鼓励妇女和在数学领域任职人数不足的其他群体成员参加，并致力于促进其所有博士后研究员的教育和职业生涯。初级数学家既受益于他们与资深学者的互动，也受益于他们从教员那里得到的指导。中级和高级数学家巩固他们的研究项目，探索新的研究方向。该学院强调统一的、跨学科的数学观点，并致力于将不同的数学家群体聚集在一起，这导致了许多意想不到的数学发展。该学院处于有利地位，能够在早期阶段确定具有重要新发展潜力的学科领域。该学院由8名常任教员领导，他们的专业知识涵盖了广泛的数学领域。作为新合作和新研究领域的中心，该学院每年接待约75名访问数学家，他们的合作研究访问通常持续4-10个月。这笔赠款资助了这些学者中的23人(17名博士后研究员和6名职业生涯中期的数学家)，他们加入了由其他来源资助的大约50名其他数学家的行列。数学学院为这个多元化的学者社区提供了一个互动的环境，丰富的数学内容和有利于合作的环境。每年，索姆管理学院都会举办一个特别的项目，重点关注一个特别令人兴奋的数学领域。未来三年的课程将是2017-2018年的“局部对称空间：分析和拓扑方面”；2018-2019年的“几何变分方法”；2019-2020年的“优化、统计和理论机器学习”。每个学期的SOM都会安排一个与专题课程相关的为期一周的工作坊，以及一个单独的为期一周的工作组。“新兴主题工作组”是一组研究人员，他们被挑选出来研究一个似乎已经成熟、可以取得重大进展的主题。其他项目包括“数学对话”，这是一个非正式的讨论小组，每周举行一次会议；以及“夏季合作者”，这是一个由受邀的研究人员组成的小组，他们在夏季的几个月里就特殊的研究项目进行合作。除了这些研讨会和项目外，SOM还定期举办研讨会、系列讲座和阅读小组。所有IAS讲座都被录制下来，并向公众开放。由助学金资助的访问数学家接受来自永久教员的个人和小组指导。他们的个人研究项目深入到以下一个或多个研究领域：分析、应用数学偏微分方程、概率、代数、代数几何、李群、表示论、微分几何、拓扑学、数学物理、动力系统、计算机科学、离散数学、理论机器学习和数论。

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.