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

该项目将支持三个系列研讨会（2016年，2017年和2018年）的物理和数学的F-理论，将轮流在弗吉尼亚理工大学，哈佛大学和佛罗里达州立大学。第一次研讨会将于2016年9月在弗吉尼亚理工大学举行。该系列讲习班将促进和促进数学和物理学的跨学科研究。 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。弦理论提供了一个竞技场，在这个竞技场中，现代数学中许多重要的和具有挑战性的问题可以联系起来，通常是以令人惊讶的和基本的方式。在这个系列研讨会中，这种形式主义将被用来研究奇异极限中的椭圆纤维流形的几何，目的是将不同的数学结构结合在一起。这些结构的范围从模空间的椭圆纤维卡-丘4-流形的奇异希钦系统;从双有理几何表示理论;并从限制混合霍奇结构的研究不变量的奇异品种。这些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联系起来的分辨率图，以及计算可能具有奇异基的纤维化的拓扑不变量;（2）在奇异几何的情况下建立Hitchin可积系统与Calabi-Yau可积系统之间的同构;（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/会议记录的形式广泛传播。 研讨会的网页是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.