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
- 来源:
- 关键词:
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.
这个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/Diffen几何和编程。我利用我在布里奇兰稳定性条件和穿越墙方面的专业知识,也使用了一些现代工具来解决这个项目,这个项目与当今纯数学中非常活跃的研究课题有关。这个项目的一半研究所谓的模(或参数)空间,它是代数几何中的基础。研究模空间的一种有效方法是跨越墙。由于越墙法在更高的维度上很容易失控,我建议将现代语言中的“派生代数几何”和“二次整数规划”的技术结合起来,使这一过程更容易处理。然后,我将用它来研究一些称为Hilbert格式的模空间。项目的另一半是通过Bridgeland稳定性条件将代数几何与微分几何和镜像对称性联系起来,从而产生一些新的Bogomolov-Gieseker型不等式(这将是将著名的Hitchin-Kobayashi类型对应扩展到Bridgeland稳定性条件的一步,这对微分几何来说是非常有趣的)。另一方面,我们进一步将它们与镜像对称性联系起来,找到了相应的“镜像不等式”,这将有助于揭示特殊的拉格朗日型方程的可解性(这在当今的辛几何中是非常重要的),也可以帮助寻找一些不能直接求解的偏微分方程组的镜像方程。桥梁稳定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,如教学、监督、面试等,这些技能对我的下一份职业生涯将是重要的,希望这将是一份好的学术工作。
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
- DOI:10.1112/plms.12577
- 发表时间:2024
- 期刊:
- 影响因子:1.8
- 作者:Rezaee F
- 通讯作者:Rezaee F
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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
- DOI:
- 发表时间:
2020 - 期刊:
- 影响因子:0
- 作者:
Fatemeh Rezaee;E. B. Samani;M. Ganjali - 通讯作者:
M. Ganjali
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
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