Local Cohomology, Differential Operators, and Determinantal Rings
局部上同调、微分算子和行列环
基本信息
- 批准号:2101671
- 负责人:
- 金额:$ 27万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2021
- 资助国家:美国
- 起止时间:2021-06-01 至 2025-05-31
- 项目状态:未结题
- 来源:
- 关键词:
项目摘要
The award is concerned with several questions in commutative algebra: this is a field that studies solution sets of polynomial equations, and the questions that will be investigated eventually yield information about the nature of the solution sets. Polynomial equations arise in a number of situations; indeed commutative algebra continues to develop a fascinating interaction with several fields, becoming an increasingly valuable tool in science and engineering. The focus here is on questions relating to differential operators, particularly in the context of rings of invariants; the differential operators may be thought of as extensions of the rules of calculus to solutions sets of polynomials, while the rings of invariants are collections of polynomials that remain unchanged under various transformations. A key part of the awarded work is the training of graduate students in topics connected with the research program.Levasseur and Stafford described the rings of differential operators on various classical invariant rings of characteristic zero; one of the projects, related to the PI's recent joint work with Jeffries, is studying the rings of differential operators on classical invariant rings in the positive characteristic case, and another is the behavior of differential operators under base change. Key tools for these come from local cohomology theory, and the study of integer torsion in local cohomology modules. Other projects involve Hankel determinantal rings, close cousins of the determinantal rings of classical invariant theory. The F-regularity of Hankel determinantal rings of positive prime characteristic will be investigated; this has an entirely equivalent formulation in terms of differential operators. The question arises naturally from the PI's joint work with Conca, Mostafazadehfard, and Varbaro, where it was proved that these rings have rational singularities.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.
该奖项涉及交换代数中的几个问题:这是一个研究多项式方程组解的领域,并且将调查的问题最终会产生有关解集性质的信息。多项式方程出现在许多情况下;事实上,交换代数继续发展与几个领域的迷人互动,成为科学和工程中越来越有价值的工具。这里的重点是与微分算子相关的问题,特别是在不变量环的背景下;微分算子可以被认为是微积分规则对多项式解集的扩展,而不变量环是多项式的集合,在各种变换下保持不变。一个关键的一部分,获奖的工作是研究生的培训主题与研究计划。Levasseur和斯塔福德描述了环的微分算子的各种经典不变环的特征零;其中一个项目,与PI最近与Jeffries的联合工作有关,是在正特征情况下研究经典不变环上的微分算子环,二是微分算子在基变化下的行为。局部上同调理论和局部上同调模中的整数挠的研究是这些问题的重要工具。其他项目涉及汉克尔行列式环,古典不变理论的行列式环的近亲。将研究具有正素特征的Hankel行列式环的F-正则性;这在微分算子方面有一个完全等价的公式。这个问题自然产生于PI与Conca、Mostafazadehfard和Varbaro的联合工作,在那里证明了这些环具有合理的奇点。这个奖项反映了NSF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(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Anurag Singh其他文献
Higher matching complexes of complete graphs and complete bipartite graphs
完全图和完全二分图的更高匹配复合体
- DOI:
10.1016/j.disc.2021.112761 - 发表时间:
2020 - 期刊:
- 影响因子:0
- 作者:
Anurag Singh - 通讯作者:
Anurag Singh
Discovery of Potent and Selective Covalent Inhibitors of HER2WT and HER2YVMA.
HER2WT 和 HER2YVMA 的强效选择性共价抑制剂的发现。
- DOI:
- 发表时间:
2024 - 期刊:
- 影响因子:7.3
- 作者:
E. Hicken;Karin Brown;Natalie C Dwulet;J. Gaudino;Erik P Hansen;Dylan P Hartley;John P Kowalski;Ellen R Laird;Nicholas C. Lazzara;Bin Li;Tung;Marie F Mutryn;Lauren Oko;Spencer P Pajk;Robert W Pipal;Rachel Z Rosen;Russell A Shelp;Anurag Singh;Jing Wang;C. E. Wise;Christina E Wong;Jim Y Wong - 通讯作者:
Jim Y Wong
The fungal ligand chitin directly binds and signals inflammation dependent on oligomer size and TLR2
真菌配体几丁质直接结合并根据寡聚体大小和 TLR2 发出炎症信号
- DOI:
10.1101/270405 - 发表时间:
2018 - 期刊:
- 影响因子:0
- 作者:
K. Fuchs;Yamel Cardona Gloria;Olaf;Franziska Herster;L. Sharma;C. Dillen;Christoph Täumer;Sabine Dickhöfer;Zsofia Bittner;Truong‐Minh Dang;Anurag Singh;Daniel Haischer;Maria A. Schlöffel;Kirsten J. Koymans;Tharmila Sanmuganantham;Milena Krach;Nadine A Schilling;F. Frauhammer;L. Miller;T. Nürnberger;S. Leibundgut;Andrea A. Gust;B. Maček;M. Frank;C. Gouttefangeas;C. D. Dela Cruz;D. Hartl;A. Weber - 通讯作者:
A. Weber
Ensemble Learning with Hybrid Modelling for Multivariate AQI, PM2.5, and PM10 Forecasting in Mumbai
使用混合建模进行集成学习,用于孟买的多元 AQI、PM2.5 和 PM10 预测
- DOI:
10.1109/cset58993.2023.10346745 - 发表时间:
2023 - 期刊:
- 影响因子:0
- 作者:
Anurag Singh;Pratham Soni;Deepa Krishnan;Ishaan Potle - 通讯作者:
Ishaan Potle
Anurag Singh的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Anurag Singh', 18)}}的其他基金
Invariant Rings, Frobenius, and Differential Operators
不变环、弗罗贝尼乌斯和微分算子
- 批准号:
2349623 - 财政年份:2024
- 资助金额:
$ 27万 - 项目类别:
Continuing Grant
Determinantal Rings, Local Cohomology, and Tight Closure
行列式环、局部上同调和紧闭
- 批准号:
1801285 - 财政年份:2018
- 资助金额:
$ 27万 - 项目类别:
Continuing Grant
Questions on Local Cohomology and Tight Closure Theory
关于局部上同调和紧闭理论的问题
- 批准号:
1500613 - 财政年份:2015
- 资助金额:
$ 27万 - 项目类别:
Standard Grant
Local cohomology, tight closure, and related questions
局部上同调、紧闭性及相关问题
- 批准号:
1162585 - 财政年份:2012
- 资助金额:
$ 27万 - 项目类别:
Standard Grant
Tight Closure, Local Cohomology, and Related Questions
紧闭、局部上同调及相关问题
- 批准号:
0600819 - 财政年份:2006
- 资助金额:
$ 27万 - 项目类别:
Standard Grant
相似海外基金
CAREER: Elliptic cohomology and quantum field theory
职业:椭圆上同调和量子场论
- 批准号:
2340239 - 财政年份:2024
- 资助金额:
$ 27万 - 项目类别:
Continuing Grant
Symplectic cohomology and quantum cohomology of Fano manifolds
Fano流形的辛上同调和量子上同调
- 批准号:
2306204 - 财政年份:2023
- 资助金额:
$ 27万 - 项目类别:
Standard Grant
Cohomology theories for algebraic varieties
代数簇的上同调理论
- 批准号:
2883661 - 财政年份:2023
- 资助金额:
$ 27万 - 项目类别:
Studentship
LEAPS-MPS: Quantum Field Theories and Elliptic Cohomology
LEAPS-MPS:量子场论和椭圆上同调
- 批准号:
2316646 - 财政年份:2023
- 资助金额:
$ 27万 - 项目类别:
Standard Grant
Cohomology of arithmetic groups in GL(2) over definite quaternion algebras
GL(2) 定四元数代数上算术群的上同调
- 批准号:
2884658 - 财政年份:2023
- 资助金额:
$ 27万 - 项目类别:
Studentship
Koszul duality and the singularity category for the enhanced group cohomology ring
增强群上同调环的 Koszul 对偶性和奇点范畴
- 批准号:
EP/W036320/1 - 财政年份:2023
- 资助金额:
$ 27万 - 项目类别:
Research Grant
Dual complexes and weight filtrations: Applications to cohomology of moduli spaces and invariants of singularities
对偶复形和权重过滤:模空间上同调和奇点不变量的应用
- 批准号:
2302475 - 财政年份:2023
- 资助金额:
$ 27万 - 项目类别:
Continuing Grant
Matrix Approximations, Stability of Groups and Cohomology Invariants
矩阵近似、群稳定性和上同调不变量
- 批准号:
2247334 - 财政年份:2023
- 资助金额:
$ 27万 - 项目类别:
Standard Grant
Research on commutative rings via etale cohomology theory
基于etale上同调理论的交换环研究
- 批准号:
23K03077 - 财政年份:2023
- 资助金额:
$ 27万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Topological Hopf Algebras and Their cyclic cohomology
拓扑 Hopf 代数及其循环上同调
- 批准号:
RGPIN-2018-04039 - 财政年份:2022
- 资助金额:
$ 27万 - 项目类别:
Discovery Grants Program - Individual