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Research in Mathematics

数学研究

基本信息

批准号：
1926686
负责人：
Akshay Venkatesh
金额：
$ 1299.95万
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：
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=1926686&HistoricalAwards=false
关键词：
Research Mathematics

项目摘要

The School of Mathematics (SoM) at the Institute for Advanced Study (IAS) seeks to support basic research and the training and development of postdoctoral researchers in mathematics. The School hosts approximately 70 researchers for long-term visits each year. Approximately one-third of these researchers are part of a special program focused on a particularly exciting field of mathematics, and the remaining are unrestricted in field. This award supports between 12 and 18 postdoctoral fellows and between 4 and 6 mid-career mathematicians annually, as well as small group collaborations during the summer. The School develops connections across career stages and mathematical fields, and an active mentoring program is in place to support postdoctoral fellows. The School also seeks to encourage researchers from underrepresented groups in the mathematical sciences to participate in its activities. The IAS as a whole brings together researchers from different institutions and fields who would not ordinarily be afforded the opportunity to interact, thereby strengthening the US scientific community as a whole. The School of Mathematics seeks to achieve its primary goals – support of fundamental research and fostering mathematical talent – by creating an environment that encourages, both formally and informally, new collaborations and new lines of research. Postdoctoral fellows are assigned two mentors – a mid-career mathematician and a faculty member or visiting senior mathematician – with whom they meet regularly. The School holds numerous specialized weekly seminars across all fields of mathematics, some jointly with Princeton University. A broadly targeted "Members Seminar" and an informal "Mathematical Conversations" event are also held weekly. Each term there is a week-long workshop associated with the special program (the topic of which is "Geometric and Modular Representation Theory" in 2021-2022, and "h-Principle and Flexibility in Geometry and PDEs" in 2022-2023). Overall, all SoM visitors benefit from an environment where they can pursue research unhampered by administrative duties.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.

高等研究院（IAS）的数学学院（SoM）旨在支持基础研究以及数学博士后研究人员的培训和发展。学院每年接待约70名研究人员进行长期访问。这些研究人员中大约有三分之一的人是一个特别项目的一部分，专注于一个特别令人兴奋的数学领域，其余的人在该领域不受限制。该奖项每年支持12至18名博士后研究员和4至6名处于职业生涯中期的数学家，以及夏季的小组合作。学院在各个职业阶段和数学领域建立联系，并有一个积极的指导计划来支持博士后。学院还寻求鼓励来自数学科学领域代表性不足群体的研究人员参与其活动。IAS作为一个整体将来自不同机构和领域的研究人员聚集在一起，这些研究人员通常没有机会进行互动，从而加强了整个美国科学界。数学学院旨在通过创造一个鼓励正式和非正式的新合作和新研究方向的环境来实现其主要目标-支持基础研究和培养数学人才。博士后研究员会被分配两名导师——一名处于职业生涯中期的数学家和一名教员或访问的高级数学家——他们会定期与导师见面。学院每周举办许多专门的研讨会，涉及数学的各个领域，有些是与普林斯顿大学联合举办的。此外，协会每周还举办“会员研讨会”和非正式的“数学对话”活动。每个学期都有一个为期一周的研讨会，与特别计划相关（2021-2022年的主题是“几何和模表示理论”，2022-2023年的主题是“几何和偏微分方程的h-原理和灵活性”）。总体而言，所有SoM访客都受益于一个不受行政职责阻碍的研究环境。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

期刊论文数量（35）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Bourgeois contact structures: Tightness, fillability and applications

布尔乔亚接触结构：密封性、填充性和应用

DOI：
10.1007/s00222-022-01131-y
发表时间：
2022
期刊：
Inventiones mathematicae
影响因子：
3.1
作者：
Bowden, Jonathan;Gironella, Fabio;Moreno, Agustin
通讯作者：
Moreno, Agustin

Enhanced dissipation and Hörmander's hypoellipticity

增强耗散和 Hörmander 的低椭圆性

DOI：
10.1016/j.jfa.2022.109522
发表时间：
2022
期刊：
Journal of Functional Analysis
影响因子：
1.7
作者：
Albritton, Dallas;Beekie, Rajendra;Novack, Matthew
通讯作者：
Novack, Matthew

Optimal-Degree Polynomial Approximations for Exponentials and Gaussian Kernel Density Estimation

指数和高斯核密度估计的最优次数多项式近似

DOI：
发表时间：
2022
期刊：
Computational complexity
影响因子：
1.4
作者：
Aggarwal, Amol and
通讯作者：
Aggarwal, Amol and

Approximate Lattices in Higher-Rank Semi-Simple Groups

高阶半简单群中的近似格

DOI：
10.1007/s00039-023-00643-w
发表时间：
2023
期刊：
Geometric and Functional Analysis
影响因子：
2.2
作者：
Machado, Simon
通讯作者：
Machado, Simon

Bounded Generation by semi-simple elements: quantitative results

半简单元素有界生成：定量结果

DOI：
10.5802/crmath.376
发表时间：
2022
期刊：
Comptes Rendus. Mathématique
影响因子：
0
作者：
Corvaja, Pietro;Demeio, Julian L.;Rapinchuk, Andrei S.;Ren, Jinbo;Zannier, Umberto M.
通讯作者：
Zannier, Umberto M.