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

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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.