Research in Geometry, String Compactifications, and Mathematical String Theory.

该奖项资助了弗吉尼亚理工学院和州立大学的埃里克·夏普教授的研究活动。镜像对称是弦理论之间的对偶性，其发现导致了物理学和数学的突破性进展。 在他的研究中，夏普教授的目标是发展镜像对称的一般化，称为“（0，2）镜像对称”，这将是一个强大的计算工具，用于理解四维理论，通过在紧致空间上卷起或“紧致化”六个维度，从弦理论中获得最小的超对称性。 该研究的一个重要部分将是进一步发展“量子层上同调”，这一概念最初由夏普教授和谢尔顿·卡茨教授提出，它计算带电物质耦合的量子修正，与这些理论的数学密切相关。该项目也将产生重大的广泛影响。 夏普教授将涉及研究生和博士后在他的研究，因此提供关键的培训，初级物理学家开始在这一领域的研究。 除了每年两次在杜克大学组织东南地区的数学弦理论会议外，他还计划组织一个关于（0，2）镜像对称性的研讨会。

This award funds the research activities of Professor Eric Sharpe at Virginia Polytechnic Institute and State University.Mirror symmetry is a duality between string theories whose discovery led to ground-breaking advances in both physics and mathematics. In his research, Professor Sharpe aims to develop a generalization of mirror symmetry, known as ``(0,2) mirror symmetry,'' which would be a powerful computational tool for understanding four-dimensional theories with minimal supersymmetry obtained from string theory by rolling up or `compactifying' six dimensions on a compact space. One significant part of that research will be to further develop `quantum sheaf cohomology,' a notion originally developed by Professors Sharpe and Sheldon Katz, which computes quantum corrections to charged matter couplings and is closely tied to the mathematics of these theories.This project will also have significant broader impacts. Professor Sharpe will involve graduate students and postdocs in his research, and so provide critical training to junior physicists beginning research in this area. In addition to organizing Southeast regional mathematical string theory meetings at Duke University twice annually, he also plans to organize a workshop on the subject of (0,2) mirror symmetry.