Wall-crossing: from classical algebraic geometry to differential geometry, mirror symmetry and derived algebraic Geometry

穿墙:从经典代数几何到微分几何、镜面对称和派生代数几何

基本信息

  • 批准号:
    EP/X032779/1
  • 负责人:
  • 金额:
    $ 35.28万
  • 依托单位:
  • 依托单位国家:
    英国
  • 项目类别:
    Fellowship
  • 财政年份:
    2023
  • 资助国家:
    英国
  • 起止时间:
    2023 至 无数据
  • 项目状态:
    未结题

项目摘要

This project involves the field of algebraic geometry and connections to other areas including algebraic topology, symplectic/diffen geometry, and programming. I use my expertise in Bridgeland stability conditions and wall-crossing, and also use some modern tools to tackle this project which is related to very active research subjects in today's pure mathematics. Half of this project studies so-called moduli (or parameter) spaces which are fundamental in algebraic geometry. One effective way to study moduli spaces is via wall-crossing. As the wall-crossing method can get easily un-controllable in higher dimensions, I propose to incorporate the technology from the modern language of "Derived Algebraic Geometry" and also "Quadratic integer Programming" to make the process more tractable. Then I will use this in studying some moduli spaces which are called Hilbert schemes. Another half of the project is connecting algebraic geometry to differential geometry and mirror symmetry via Bridgeland stability conditions to produce some new Bogomolov-Gieseker type inequalities (which will be a step towards extending the celebrated Hitchin-Kobayashi type correspondence to Bridgeland stability conditions, which is very interesting to differential geometers). On the other hand, we take a further step and relate these to mirror symmetry via finding some corresponding "mirror inequalities", which in turn would shed light on the solvability of special Lagrangian type equations (which are very important to symplectic geometers these days), and also could help to find mirror equations to some Partial Differential Equations which cannot be tackled directly. The theory of Bridgeland stability is well established in Europe and the applications as above are considered as cutting edge in the area. During this fellowship, I will also learn other skills e.g. teaching, supervision, interviewing, etc, which will be important for my next career which will be hopefully a good academic job.
该项目涉及代数几何领域以及与其他领域的联系,包括代数拓扑、辛/微分几何和编程。我利用我在布里奇兰稳定性条件和穿墙方面的专业知识,并使用一些现代工具来解决这个项目,该项目与当今纯数学中非常活跃的研究课题相关。该项目的一半研究所谓的模(或参数)空间,这是代数几何的基础。研究模空间的一种有效方法是穿墙。由于穿墙方法在更高维度上很容易变得不可控,因此我建议结合现代语言“派生代数几何”和“二次整数规划”中的技术,使过程更容易处理。然后我将用它来研究一些称为希尔伯特方案的模空间。该项目的另一半是通过 Bridgeland 稳定条件将代数几何与微分几何和镜像对称联系起来,以产生一些新的 Bogomolov-Gieseker 型不等式(这将是将著名的 Hitchin-Kobayashi 型对应扩展到 Bridgeland 稳定条件的一步,这对微分几何学家来说非常有趣)。另一方面,我们更进一步,通过找到一些相应的“镜像不等式”将它们与镜像对称联系起来,这反过来又会揭示特殊拉格朗日型方程(这对当今的辛几何学家非常重要)的可解性,并且还可以帮助找到一些无法直接求解的偏微分方程的镜像方程。布里奇兰稳定性理论在欧洲已经很成熟,上述应用被认为是该领域的前沿。在这次奖学金期间,我还将学习其他技能,例如教学、监督、面试等,这对我的下一个职业很重要,希望能成为一份好的学术工作。

项目成果

期刊论文数量(1)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Geometry of canonical genus 4 curves
规范4曲线的几何
{{ 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 }}

Fatemeh Rezaee其他文献

Constructing smoothings of stable maps
构建稳定地图的平滑
  • DOI:
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Fatemeh Rezaee;Mohan Swaminathan
  • 通讯作者:
    Mohan Swaminathan
Development of radiolabeled radachlorin complex as a possible tumor targeting agent
  • DOI:
    10.1007/s10967-014-3645-5
  • 发表时间:
    2014-10-05
  • 期刊:
  • 影响因子:
    1.600
  • 作者:
    Yousef Fazaeli;Amir R. Jalilian;Fatemeh Rezaee;Tahereh Firouzyar;Sedigheh Moradkhani;Azar Bagheri;Abbas Majdabadi
  • 通讯作者:
    Abbas Majdabadi
Gaussian copula-based zero-inflated power series joint models to analyze correlated count data
基于高斯 copula 的零膨胀幂级数联合模型来分析相关计数数据
Highly effective and regioselective Michael addition of indoles to α,β-unsaturated ketones promoted by pentafluorophenylammonium triflate
五氟苯三氟甲磺酸铵促进吲哚与 α,β-不饱和酮的高效区域选择性迈克尔加成
  • DOI:
    10.1016/j.crci.2012.08.002
  • 发表时间:
    2013
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Samad Khaksar;S. M. Vahdat;Fatemeh Rezaee
  • 通讯作者:
    Fatemeh Rezaee
The phytochemical study and antiprolifrative effect of hydroalcoholic extract of Adiantum capillus-veneris L. on MCF-7 and MRC-5 cell lines
铁线蕨水醇提取物的植物化学研究及其对 MCF-7 和 MRC-5 细胞系的抗增殖作用
  • DOI:
    10.29252/nbr.5.2.118
  • 发表时间:
    2018
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Hesane Hassanpour;Mohammad Shokrzadeh Lamuki;R. Tabari;Fatemeh Rezaee;Fatereh Rezaee
  • 通讯作者:
    Fatereh Rezaee

Fatemeh Rezaee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 }}

相似国自然基金

Wall crossing现象和内禀Higgs态
  • 批准号:
    11305125
  • 批准年份:
    2013
  • 资助金额:
    22.0 万元
  • 项目类别:
    青年科学基金项目

相似海外基金

Crossing the Finish Line: Intervening in a Critical Period for Educational Investment
冲过终点线:介入教育投资关键期
  • 批准号:
    2343873
  • 财政年份:
    2024
  • 资助金额:
    $ 35.28万
  • 项目类别:
    Standard Grant
Motivic invariants and birational geometry of simple normal crossing degenerations
简单正态交叉退化的动机不变量和双有理几何
  • 批准号:
    EP/Z000955/1
  • 财政年份:
    2024
  • 资助金额:
    $ 35.28万
  • 项目类别:
    Research Grant
ARCHCROP: Crossing Paths: Millet, Wheat and Cultural Exchanges in the Inner Asian Mountain Corridor, China
ARCHCROP:交叉路径:中国内亚山地走廊的小米、小麦和文化交流
  • 批准号:
    EP/Y027809/1
  • 财政年份:
    2024
  • 资助金额:
    $ 35.28万
  • 项目类别:
    Fellowship
Unobtrusive Technologies for Secure and Seamless Border Crossing for Travel Facilitation
用于安全、无缝过境的低调技术,为旅行提供便利
  • 批准号:
    10070292
  • 财政年份:
    2023
  • 资助金额:
    $ 35.28万
  • 项目类别:
    EU-Funded
The theoretical and practical study on the "boundary-crossing" nature of school education for social jusitice
学校社会正义教育“跨界”性的理论与实践研究
  • 批准号:
    23K02191
  • 财政年份:
    2023
  • 资助金额:
    $ 35.28万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Phosphodiesterase 4B Inhibition as a Therapeutic Target for Alcohol-associated Liver Disease
磷酸二酯酶 4B 抑制作为酒精相关性肝病的治疗靶点
  • 批准号:
    10354185
  • 财政年份:
    2023
  • 资助金额:
    $ 35.28万
  • 项目类别:
Metal-free, genetically encoded reporters for calcium recording with MRI
用于 MRI 钙记录的无金属基因编码报告基因
  • 批准号:
    10660042
  • 财政年份:
    2023
  • 资助金额:
    $ 35.28万
  • 项目类别:
Targeted immunotherapy for amyotrophic lateral sclerosis and frontotemporal dementia
肌萎缩侧索硬化症和额颞叶痴呆的靶向免疫治疗
  • 批准号:
    10759808
  • 财政年份:
    2023
  • 资助金额:
    $ 35.28万
  • 项目类别:
Peripherally-restricted non-addictive cannabinoids for cancer pain treatment
用于癌症疼痛治疗的外周限制性非成瘾大麻素
  • 批准号:
    10726405
  • 财政年份:
    2023
  • 资助金额:
    $ 35.28万
  • 项目类别:
Preservation of brain NAD+ as a novel non-amyloid based therapeutic strategy for Alzheimer’s disease
保留大脑 NAD 作为阿尔茨海默病的一种新型非淀粉样蛋白治疗策略
  • 批准号:
    10588414
  • 财政年份:
    2023
  • 资助金额:
    $ 35.28万
  • 项目类别:
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了