A Three-Workshop Series on the Mathematics and Physics of F-theory

F 理论数学和物理三期研讨会系列

• 批准号: 1603247
• 负责人: Lara Anderson
• 金额: $ 5万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-06-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1603247&HistoricalAwards=false
• 关键词: Three; Workshop; Series; Mathematics; Physics

This project will support a three workshop series (in 2016, 2017, and 2018) on the Physics and Mathematics of F-theory that will rotate between Virginia Tech, Harvard University and Florida State University. The first workshop will be held in September 2016 at Virginia Tech. The workshop series will promote and facilitate interdisciplinary research in mathematics and physics. These workshops will bring together researchers from a diverse range of institutions and backgrounds to address pressing problems at the interface of algebraic/differential geometry and string theory. The meetings will include junior participants and members of under-represented groups in the sciences.String theory provides an arena in which many significant and challenging questions in modern mathematics can be linked, often in surprising and fundamental ways. In this workshop series, this formalism will be utilized to study the geometry of elliptically fibered manifolds in singular limits, with the goal of bringing together diverse mathematical structures. These structures range from the moduli spaces of elliptically fibered Calabi-Yau 4-manifolds to those of singular Hitchin systems; from birational geometry to representation theory; and from limiting mixed Hodge structures to the study of invariants of singular varieties. The programs will involve several areas of investigation: (1) Resolution graphs relating the structure of singular fibers to representation-theoreticinvariants, and computing topological invariants of fibrations with possibly singular base; (2) Establishing isomorphisms between the Hitchin integrable system and that of the Calabi-Yau integrable system in the case of singular geometry; and (3) Geometries of (1,0) Conformal Field Theories. The broader impacts of this workshop series will include the training of graduate students and the interdisciplinary results of the workshops which will be widely disseminated in the form of monographs/proceedings. The workshop webpage is http://www.phys.vt.edu/~lara137/ftheory.html.

该项目将支持F弗吉尼亚理工学院，哈佛大学和佛罗里达州立大学之间轮换的F理论物理和数学的三个研讨会系列（2016年，2017年和2018年）。第一个研讨会将于2016年9月在弗吉尼亚理工大学举行。研讨会系列将促进和促进数学和物理学的跨学科研究。 这些研讨会将使来自各种机构和背景的研究人员聚集在一起，以解决代数/差异几何和弦理论界面上的紧迫问题。会议将包括科学中的初级参与者和代表性不足的群体的成员。斯特林理论提供了一个竞技场，在该舞台上，现代数学中的许多重大且具有挑战性的问题通常可以以令人惊讶和基本的方式联系起来。在这个研讨会的系列中，这种形式主义将用于研究奇异界限的椭圆纤维歧管的几何形状，目的是将各种数学结构融合在一起。这些结构的范围从椭圆形的纤维纤维卡拉比（Calabi-Yau）4个manifolds到奇异hitchin系统的模量范围；从外表几何到表示理论； 从限制混合的猪结构到对奇异品种不变的研究。该程序将涉及一些调查领域：（1）分辨率图将单数纤维与表示理论引导的结构以及计算具有奇异碱基的纤维的拓扑不变性； （2）在奇异几何形状的情况下，建立Hitchin可集成系统与Calabi-Yau集成系统之间的同构； （3）（1,0）保形场理论的几何形状。该研讨会系列的更广泛的影响将包括对研究生的培训以及研讨会的跨学科结果，这些结果将以专着/诉讼的形式广泛传播。 研讨会网页是http://www.phys.vt.edu/~lara137/ftheory.html。