CAREER: New methods in curve counting
职业:曲线计数的新方法
基本信息
- 批准号:2239320
- 负责人:
- 金额:$ 41.71万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2023
- 资助国家:美国
- 起止时间:2023-07-01 至 2024-03-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The past thirty years have seen a deep and surprising interplay between several branches in pure mathematics, and string theory in physics. In particular, physical predictions have led to the development of mathematical invariants which count algebraic curves in spaces, and conversely, the mathematical study of these invariants has led to advances in string theory. This project further develops two curve counting techniques, the "logarithmic gauged linear sigma model" (log GLSM) and "quasimaps", and their combination, with the goal of making progress on challenging conjectures from physics, which have appeared out of reach of mathematicians until recently. This project will offer ample training opportunities for graduate students and postdocs. In addition, the PI will organize a yearly intensive weekend learning workshop on a topic of interest, as well as organize events aiming to counter stereotypes in STEM.More specifically, the project will result in a proof of the localization formula for log GLSM, which is of utmost importance for the application of this technique. In addition, effective invariants, which are a major ingredient of the localization formula, will be studied. In a different direction, the PI will explore applications of log GLSM to the tautological ring, to establish structural predictions observed in physics, such as the "conifold gap condition", for the quintic threefold and other one-parameter Calabi-Yau threefolds, and to establish the Landau-Ginzburg/Calabi-Yau correspondence for quintic threefolds in all genera. With regard to quasi-maps, the second main technique employed in this project, the PI will use quasi-maps for explicit computations of Gromov-Witten invariants of non-convex complete intersections. Quasi-maps appear necessary for approaching some of the more mysterious predictions from physics, and hence log GLSM will be extended to allow for quasi-maps.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.
在过去的三十年里,纯数学中的几个分支和物理学中的弦理论之间有着深刻而令人惊讶的相互作用。特别是,物理预测导致了计算空间中代数曲线的数学不变量的发展,反过来,这些不变量的数学研究导致了弦理论的进步。该项目进一步发展了两种曲线计数技术,即“对数测量线性西格玛模型”(log GLSM)和“准映射”,以及它们的组合,目标是在挑战物理学中的猜想方面取得进展,这些猜想直到最近才出现在数学家的范围之外。本项目将为研究生和博士后提供充足的培养机会。此外,PI将组织每年一次关于感兴趣主题的周末密集学习研讨会,并组织旨在消除STEM刻板印象的活动。更具体地说,该项目将得到测井GLSM定位公式的证明,这对该技术的应用至关重要。此外,还将研究局部化公式的主要组成部分——有效不变量。在不同的方向上,PI将探索对数GLSM在同音环中的应用,建立物理上观察到的结构预测,如五次三次和其他单参数Calabi-Yau三次的“confold gap条件”,并建立所有属的五次三次的Landau-Ginzburg/Calabi-Yau对应关系。关于拟映射,在这个项目中采用的第二种主要技术,PI将使用拟映射来显式计算非凸完全交的Gromov-Witten不变量。准映射对于接近一些来自物理学的更神秘的预测似乎是必要的,因此log GLSM将被扩展以允许准映射。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(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 }}
Felix Janda其他文献
Gromov--Witten invariants with naive tangency conditions
格罗莫夫--具有朴素相切条件的维滕不变量
- DOI:
- 发表时间:
2023 - 期刊:
- 影响因子:0
- 作者:
Felix Janda;Tony Yue Yu - 通讯作者:
Tony Yue Yu
Felix Janda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('Felix Janda', 18)}}的其他基金
CAREER: New methods in curve counting
职业:曲线计数的新方法
- 批准号:
2422291 - 财政年份:2024
- 资助金额:
$ 41.71万 - 项目类别:
Continuing Grant
Logarithmic Gauged Linear Sigma Models
对数测量线性西格玛模型
- 批准号:
2054830 - 财政年份:2020
- 资助金额:
$ 41.71万 - 项目类别:
Standard Grant
Logarithmic Gauged Linear Sigma Models
对数测量线性西格玛模型
- 批准号:
1901748 - 财政年份:2019
- 资助金额:
$ 41.71万 - 项目类别:
Standard Grant
相似海外基金
CAREER: New methods in curve counting
职业:曲线计数的新方法
- 批准号:
2422291 - 财政年份:2024
- 资助金额:
$ 41.71万 - 项目类别:
Continuing Grant
CAREER: Acceleration Methods, Iterative Solvers and Heterogeneous Architectures: The New Landscape of Large-Scale Scientific Simulations
职业:加速方法、迭代求解器和异构架构:大规模科学模拟的新景观
- 批准号:
2324958 - 财政年份:2023
- 资助金额:
$ 41.71万 - 项目类别:
Continuing Grant
CAREER: Hybrid Approaches to Quantum Cryptography: New Methods and Protocols
职业:量子密码学的混合方法:新方法和协议
- 批准号:
2143644 - 财政年份:2022
- 资助金额:
$ 41.71万 - 项目类别:
Continuing Grant
CAREER: New Methods for Central Streaming Problems
职业:解决中央流媒体问题的新方法
- 批准号:
2244899 - 财政年份:2022
- 资助金额:
$ 41.71万 - 项目类别:
Continuing Grant
CAREER: Acceleration Methods, Iterative Solvers and Heterogeneous Architectures: The New Landscape of Large-Scale Scientific Simulations
职业:加速方法、迭代求解器和异构架构:大规模科学模拟的新景观
- 批准号:
2144181 - 财政年份:2022
- 资助金额:
$ 41.71万 - 项目类别:
Continuing Grant
CAREER: Developing New Computational Methods to Address the Missing Data Problem in Population Genomics
职业:开发新的计算方法来解决群体基因组学中的缺失数据问题
- 批准号:
2147812 - 财政年份:2021
- 资助金额:
$ 41.71万 - 项目类别:
Continuing Grant
CAREER: Developing New Computational Methods to Address the Missing Data Problem in Population Genomics
职业:开发新的计算方法来解决群体基因组学中的缺失数据问题
- 批准号:
2042516 - 财政年份:2021
- 资助金额:
$ 41.71万 - 项目类别:
Continuing Grant
CAREER: New Methods for the Synthesis of Nitrogen-Containing Heterocycles
职业:含氮杂环合成新方法
- 批准号:
1845219 - 财政年份:2019
- 资助金额:
$ 41.71万 - 项目类别:
Continuing Grant
CAREER: New Methods and Applications for Smooth Rigidity of Algebraic Actions
职业:代数动作的平滑刚性的新方法和应用
- 批准号:
1845416 - 财政年份:2019
- 资助金额:
$ 41.71万 - 项目类别:
Continuing Grant
Early-Career Participant Support: The 13th International Conference on Numerical Methods in Industrial Forming Processes (NUMIFORM); Portsmouth, New Hampshire; June 23-27, 2019
早期职业参与者支持:第 13 届工业成形过程数值方法国际会议 (NUMIFORM);
- 批准号:
1916600 - 财政年份:2019
- 资助金额:
$ 41.71万 - 项目类别:
Standard Grant