Algebraic Geometry and Strings

几十年来，对物理理论（弦理论和量子场论）与数学（特别是代数几何）相互作用的探索已经非常富有成效，而且这种工具和方法的结合的力量似乎只会随着时间的推移而加强。本项目的目标是探索和推进代数几何与弦理论和量子场论之间的一些主要问题。该研究将采用并结合代数几何、拓扑、可积系统、弦理论和量子场论等多种技术。该项目还包括许多更广泛的影响活动，如指导和组织会议和学校，成为国际董事会和评奖委员会的成员，修改宾夕法尼亚大学的研究生课程，研究生和本科生的课程发展，为博士后、研究生和本科生提供建议，编辑几本公共服务卷，编辑期刊和论文集。更具体地说，该项目包括，除其他主题外：通过非阿贝尔霍奇理论对几何朗兰兹猜想的qft启发攻击；根据希钦系统的变化对S类物理理论的数学研究；超几何思想在弦理论高环计算中的应用探索代数几何中的模问题，其中一些是由QFT猜想引起的，另一些纯粹是代数几何中的问题；进一步探索F理论的各个方面，建立F理论的数学基础；探索范畴对称和缺陷对称tft。这些特定研究领域中的每一个都代表了数学和/或物理学中的一个重大开放问题，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。

Exploration of the interactions of physical theories (string theory and quantum field theory) with mathematics (especially algebraic geometry) has been extremely productive for decades, and the power of this combination of tools and approaches only seems to strengthen with time. 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 steering and organization of conferences and schools, membership of international boards and prize committees, revising Penn’s graduate program, curricular development at the graduate and undergraduate level, advising postdocs, graduate and undergraduate students, editing several public service volumes and editing of journals and proceedings volumes.More specifically, the project includes, among other topics: a QFT-inspired attack on the geometric Langlands conjecture via non-abelian Hodge theory; a mathematical investigation of physical Theories of class S in terms of variations of Hitchin systems; applications of ideas from supergeometry to higher loop calculations in string theory; exploration of moduli questions in algebraic geometry, some of them motivated by a QFT conjecture, others purely within algebraic geometry; further exploration of aspects of F theory and establishment of its mathematical foundations; and exploration of categorical symmetries and defect symmetry TFTs. 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.