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

该项目将支持关于f理论的物理和数学的三个系列研讨会（2016年、2017年和2018年），这些研讨会将在弗吉尼亚理工大学、哈佛大学和佛罗里达州立大学之间轮流举行。首届研讨会将于2016年9月在弗吉尼亚理工大学举行。该系列研讨会将促进和促进数学和物理的跨学科研究。这些研讨会将汇集来自不同机构和背景的研究人员，以解决代数/微分几何和弦理论界面的紧迫问题。这些会议将包括初级与会者和科学界代表性不足的群体的成员。弦理论提供了一个舞台，在这个舞台上，现代数学中许多重要和具有挑战性的问题可以以令人惊讶和基本的方式联系起来。在这个研讨会系列中，这个形式将被用来研究椭圆纤维流形在奇异极限下的几何，目的是将不同的数学结构结合在一起。这些结构的范围从椭圆光纤Calabi-Yau - 4流形的模空间到奇异Hitchin系统的模空间；从二元几何到表征理论从限制混合Hodge结构到奇异变量的不变量研究。该计划将涉及几个研究领域：(1)将奇异纤维的结构与表示理论不变量相关的分辨率图，以及计算可能具有奇异基的纤维的拓扑不变量；(2)在奇异几何条件下建立了Hitchin可积系统与Calabi-Yau可积系统的同构；(3)（1,0）共形场论的几何。这一系列讲习班的更广泛影响将包括培训研究生和讲习班的跨学科成果，这些成果将以专著/论文集的形式广泛传播。工作坊网页为http://www.phys.vt.edu/~lara137/ftheory.html。

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.