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.

该项目的目标是探索和推进代数几何与弦理论和量子场论接口的一些重大问题。这项研究将采用和联合收割机从代数几何，拓扑，可积系统，弦理论和量子场论的各种技术。该项目还包括许多更广泛的影响活动，如研究生和本科生课程开发，以及博士后，研究生和本科生的研究培训机会。几十年来，弦理论和量子场论与代数几何的相互作用的探索一直非常富有成效，这种工具和方法的组合的力量似乎只会随着时间的推移而加强。在这个项目中，PI计划进行：（1）通过非阿贝尔Hodge理论对几何Langlands猜想的量子场论启发的攻击;（2）根据Hitchin系统的变化对最近发现的S类物理理论进行数学研究;（3）将超几何的思想应用于弦理论中的高级循环计算;（4）探索代数几何中的模问题，其中一些是由量子场论猜想引起的，另一些纯粹是在代数几何中;（5）将他的Calabi-Yau可积系统的构造扩展到亚纯和抛物版本，实现了希钦的系统;（6）进一步探讨F-理论的各个方面，建立F-理论的数学基础。每个特定的研究领域都代表了数学和/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

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