Research in Mathematical Physics and Algebraic Geometry

数学物理与代数几何研究

• 批准号: 2001673
• 负责人: Ron Donagi
• 金额: $ 52万
• 依托单位: University of Pennsylvania
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-07-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2001673&HistoricalAwards=false
• 关键词: Research; Mathematical; Physics; Algebraic; Geometry

The goal of this project is to explore and push forward some of the major issues at the interface of algebraic geometry with string theory and quantum field theory. The research will employ and combine a variety of techniques from algebraic geometry, topology, integrable systems, string theory, and quantum field theory. The project also includes many broader impact activities such as curricular development at the graduate and undergraduate level, and research training opportunities for postdocs, graduate and undergraduate students. Exploration of the interactions of string theory and quantum field theory with algebraic geometry has been extremely productive for decades, and the power of this combination of tools and approaches only seems to strengthen with time. In this project, the PI plans to carry out: (1) a quantum field theory-inspired attack on the geometric Langlands conjecture via non-abelian Hodge theory; (2) a mathematical investigation of the recently discovered physical theories of class S in terms of variations of Hitchin systems; (3) applications of ideas from supergeometry to higher loop calculations in string theory; (4) exploration of moduli questions in algebraic geometry, some of them motivated by a quantum field theory conjecture, others purely within algebraic geometry; (5) extension of his construction of Calabi-Yau integrable systems realizing Hitchin's system to meromorphic and parabolic versions; and (6) further exploration of aspects of F-theory and establishment of its mathematical foundations. Each of these specific research areas represents a major open problem in math and/or in physics, whose solution will make a major contribution to the field.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.

该项目的目的是通过字符串理论和量子场理论探索和推动代数几何界面的一些主要问题。该研究将采用并结合来自代数几何，拓扑，可集成系统，弦理论和量子场理论的各种技术。该项目还包括许多更广泛的影响活动，例如研究生和本科生的课程发展，以及研究生，研究生和本科生的研究培训机会。数十年来，探索字符串理论与量子场理论与代数几何形状的相互作用一直非常有效，工具和方法组合的力量似乎只会随着时间的推移而增强。在该项目中，PI计划进行：（1）通过非亚伯式霍奇理论对量子场理论启发的量子攻击； （2）关于希钦系统的变化，对最近发现的S类物理理论的数学研究； （3）在字符串理论中，从超级几何到较高循环计算的思想应用； （4）对代数几何形状中模量问题的探索，其中一些是由量子场理论猜想的，而另一些则纯粹是在代数几何内； （5）扩展了他的Calabi-Yau集成系统的构建，该系统将Hitchin的系统实现为Meromorormormorphic和抛物线版本； （6）进一步探索F理论的各个方面和建立其数学基础。这些特定的研究领域中的每一个都代表了数学和/或物理学中的一个主要开放问题，其解决方案将对该领域做出重大贡献。该奖项反映了NSF的法定任务，并认为使用基金会的知识分子和更广泛的影响评估标准，认为值得通过评估来获得支持。

项目成果

Brill-Noether-general limit root bundles: absence of vector-like exotics in F-theory Standard Models

Brill-Noether 一般极限根丛：F 理论标准模型中不存在类似矢量的奇异值

• DOI: 10.1007/jhep11(2022)004
• 发表时间: 2022
• 期刊: Journal of High Energy Physics
• 影响因子: 5.4
• 作者: Bies, Martin;Cvetič, Mirjam;Donagi, Ron;Ong, Marielle
• 通讯作者: Ong, Marielle

The bad locus in the moduli of super Riemann surfaces with Ramond punctures

具有雷蒙德穿孔的超级黎曼曲面模量的坏轨迹

• DOI: 10.1016/j.geomphys.2023.104765
• 发表时间: 2023
• 期刊: Journal of Geometry and Physics
• 影响因子: 1.5
• 作者: Donagi, Ron;Ott, Nadia
• 通讯作者: Ott, Nadia