Research in Mathematics

高等研究院（IAS）的数学学院（SoM）有两个主要目标。首先，它支持数学的基础研究，鼓励原创思维，并产生重大的知识进步。其次，它投资于培养多样化的数学人才。学院强烈鼓励女性和其他在数学领域代表性不足的群体成员的参与，并致力于促进所有博士后研究员的教育和职业发展。初级数学家受益于他们与资深学者的互动和他们从教师那里得到的指导。中高级数学家巩固自己的研究项目，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。在早期阶段，学院在识别具有重要新发展潜力的学科领域方面处于有利地位。该学院由八名全职教师领导，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，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。该基金资助了其中23位学者（17位博士后和6位处于职业生涯中期的数学家），另外还有大约50位数学家得到了其他来源的资助。它还提供资金，在夏季举办小型合作小组。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，有利于合作。每年SoM都会开展一个特别的项目，专注于一个特别令人兴奋的数学领域。未来三年的项目为2017-2018年的“局部对称空间：解析和拓扑方面”；2018-2019《几何变分方法》；2019-2020年“优化、统计和理论机器学习”。每学期SoM都会举办一个为期一周的专题研讨会，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”（每周一次的非正式讨论小组）和“夏季合作者”（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，SoM还提供定期研讨会、系列讲座和阅读小组。国际会计准则的所有讲座都有录像，并向公众开放。获得资助的访问数学家将接受长期教员的个人和小组指导。他们的个人研究项目涉及以下一个或多个研究领域：分析、应用数学偏微分方程、概率论、代数、代数几何、李群、表示理论、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.