FRG: Collaborative Research: Algebraic Geometry and Singularities in Positive and Mixed Characteristic
FRG:合作研究:代数几何和正特征和混合特征中的奇点
基本信息
- 批准号:2139613
- 负责人:
- 金额:$ 13.67万
- 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:2021-05-01 至 2024-05-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Algebraic Geometry studies algebraic varieties which are geometric objects defined by polynomial equations. One of the most natural problems in this area is to understand the singularities that naturally occur when considering algebraic varieties and how these singularities influence the global geometry of algebraic varieties. In recent years there have been a number of breakthroughs, especially in the case where we consider solutions over the complex numbers. At the same time new techniques and approaches have emerged for studying solutions in positive and mixed characteristics. The primary goal of this collaborative project is to advance and unify these ideas to further understand and solve some of the most challenging programs in both local and global algebraic geometry. In addition the project provides research training opportunities for graduate students. The PIs will investigate singularities in positive and mixed characteristics by using a variety of techniques including those arising from the minimal model program, from the theory of F-singularities, and from Scholze's work on perfectoid algebras and spaces. The PIs will also organize workshops, a summer school and a conference, aimed at training young researchers in this area, disseminating recent results and facilitating further advances and breakthroughs.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.
代数几何学研究的是代数簇,它是由多项式方程定义的几何对象。在这一领域最自然的问题之一是理解奇异性,自然发生时,考虑代数簇和这些奇异性如何影响全球几何的代数簇。近年来有一些突破,特别是在我们考虑复数的解决方案的情况下。与此同时,出现了新的技术和方法来研究解决方案的积极和混合的特点。这个合作项目的主要目标是推进和统一这些想法,以进一步理解和解决局部和全局代数几何中一些最具挑战性的程序。此外,该项目还为研究生提供研究培训机会。该PI将调查奇点的积极和混合的特点,通过使用各种技术,包括那些所产生的最小模型计划,从理论的F-奇点,并从Scholze的工作perfectoid代数和空间。该奖项反映了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(5)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Uniqueness of the minimizer of the normalized volume function
- DOI:10.4310/cjm.2021.v9.n1.a2
- 发表时间:2020-05
- 期刊:
- 影响因子:1.6
- 作者:Chenyang Xu-;Ziquan Zhuang
- 通讯作者:Chenyang Xu-;Ziquan Zhuang
Finite generation for valuations computing stability thresholds and applications to K-stability
- DOI:10.4007/annals.2022.196.2.2
- 发表时间:2021-02
- 期刊:
- 影响因子:4.9
- 作者:Yuchen Liu;Chenyang Xu;Ziquan Zhuang
- 通讯作者:Yuchen Liu;Chenyang Xu;Ziquan Zhuang
Openness of K-semistability for Fano varieties
- DOI:10.1215/00127094-2022-0054
- 发表时间:2019-07
- 期刊:
- 影响因子:2.5
- 作者:Harold Blum;Yuchen Liu;Chenyang Xu-
- 通讯作者:Harold Blum;Yuchen Liu;Chenyang Xu-
K-stability of Fano varieties: an algebro-geometric approach
- DOI:10.4171/emss/51
- 发表时间:2020-11
- 期刊:
- 影响因子:2.3
- 作者:Chenyang Xu
- 通讯作者:Chenyang Xu
{{
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 }}
Chenyang Xu其他文献
Recent Advances in DNA Repair Pathway and Its Application in Personalized Care of Metastatic Castration-Resistant Prostate Cancer (mCRPC).
DNA 修复途径的最新进展及其在转移性去势抵抗性前列腺癌 (mCRPC) 个体化护理中的应用。
- DOI:
- 发表时间:
2020 - 期刊:
- 影响因子:0
- 作者:
Chenyang Xu;Shanhua Mao;Haowen Jiang - 通讯作者:
Haowen Jiang
Effectiveness of the log Iitaka fibration for 3-folds and 4-folds
3 倍和 4 倍对数 Iitaka 纤维化的有效性
- DOI:
10.2140/ant.2009.3.697 - 发表时间:
2009 - 期刊:
- 影响因子:1.3
- 作者:
Gueorgui Todorov;Chenyang Xu - 通讯作者:
Chenyang Xu
Multi‑index base‑stock policy for inventory systems with multiple capacitated suppliers
具有多个供应商的库存系统的多指数基础库存策略
- DOI:
10.1007/s00291-021-00658-5 - 发表时间:
2021 - 期刊:
- 影响因子:2.7
- 作者:
Chaolin Yang;Diyuan Huang;Chenyang Xu - 通讯作者:
Chenyang Xu
A summary of geometric level-set analogues for a general class of parametric active contour and surface models
一般类参数化活动轮廓和曲面模型的几何水平集类似物总结
- DOI:
10.1109/vlsm.2001.938888 - 发表时间:
2001 - 期刊:
- 影响因子:0
- 作者:
Chenyang Xu;A. Yezzi;Jerry L Prince - 通讯作者:
Jerry L Prince
Rational points of rationally simply connected varieties over global function fields
全局函数域上有理单连通簇的有理点
- DOI:
10.5802/ahl.65 - 发表时间:
2017 - 期刊:
- 影响因子:0
- 作者:
J. Starr;Chenyang Xu - 通讯作者:
Chenyang Xu
Chenyang Xu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('Chenyang Xu', 18)}}的其他基金
K-Stability in Higher Dimensional Geometry
高维几何中的 K 稳定性
- 批准号:
2201349 - 财政年份:2022
- 资助金额:
$ 13.67万 - 项目类别:
Continuing Grant
K-stability and Higher Dimensional Geometry
K 稳定性和高维几何
- 批准号:
2153115 - 财政年份:2021
- 资助金额:
$ 13.67万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Algebraic Geometry and Singularities in Positive and Mixed Characteristic
FRG:合作研究:代数几何和正特征和混合特征中的奇点
- 批准号:
1952531 - 财政年份:2020
- 资助金额:
$ 13.67万 - 项目类别:
Continuing Grant
K-stability and Higher Dimensional Geometry
K 稳定性和高维几何
- 批准号:
1901849 - 财政年份:2019
- 资助金额:
$ 13.67万 - 项目类别:
Continuing Grant
相似海外基金
FRG: Collaborative Research: New birational invariants
FRG:协作研究:新的双有理不变量
- 批准号:
2244978 - 财政年份:2023
- 资助金额:
$ 13.67万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Singularities in Incompressible Flows: Computer Assisted Proofs and Physics-Informed Neural Networks
FRG:协作研究:不可压缩流中的奇异性:计算机辅助证明和物理信息神经网络
- 批准号:
2245017 - 财政年份:2023
- 资助金额:
$ 13.67万 - 项目类别:
Standard Grant
FRG: Collaborative Research: Variationally Stable Neural Networks for Simulation, Learning, and Experimental Design of Complex Physical Systems
FRG:协作研究:用于复杂物理系统仿真、学习和实验设计的变稳定神经网络
- 批准号:
2245111 - 财政年份:2023
- 资助金额:
$ 13.67万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Variationally Stable Neural Networks for Simulation, Learning, and Experimental Design of Complex Physical Systems
FRG:协作研究:用于复杂物理系统仿真、学习和实验设计的变稳定神经网络
- 批准号:
2245077 - 财政年份:2023
- 资助金额:
$ 13.67万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Singularities in Incompressible Flows: Computer Assisted Proofs and Physics-Informed Neural Networks
FRG:协作研究:不可压缩流中的奇异性:计算机辅助证明和物理信息神经网络
- 批准号:
2244879 - 财政年份:2023
- 资助金额:
$ 13.67万 - 项目类别:
Standard Grant
FRG: Collaborative Research: New Birational Invariants
FRG:合作研究:新的双理性不变量
- 批准号:
2245171 - 财政年份:2023
- 资助金额:
$ 13.67万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Singularities in Incompressible Flows: Computer Assisted Proofs and Physics-Informed Neural Networks
FRG:协作研究:不可压缩流中的奇异性:计算机辅助证明和物理信息神经网络
- 批准号:
2403764 - 财政年份:2023
- 资助金额:
$ 13.67万 - 项目类别:
Standard Grant
FRG: Collaborative Research: Singularities in Incompressible Flows: Computer Assisted Proofs and Physics-Informed Neural Networks
FRG:协作研究:不可压缩流中的奇异性:计算机辅助证明和物理信息神经网络
- 批准号:
2245021 - 财政年份:2023
- 资助金额:
$ 13.67万 - 项目类别:
Standard Grant
FRG: Collaborative Research: Variationally Stable Neural Networks for Simulation, Learning, and Experimental Design of Complex Physical Systems
FRG:协作研究:用于复杂物理系统仿真、学习和实验设计的变稳定神经网络
- 批准号:
2245097 - 财政年份:2023
- 资助金额:
$ 13.67万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Variationally Stable Neural Networks for Simulation, Learning, and Experimental Design of Complex Physical Systems
FRG:协作研究:用于复杂物理系统仿真、学习和实验设计的变稳定神经网络
- 批准号:
2245147 - 财政年份:2023
- 资助金额:
$ 13.67万 - 项目类别:
Continuing Grant