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

该奖项资助弗吉尼亚理工学院和州立大学埃里克·夏普教授的研究活动。镜像对称是弦理论之间的一种对偶，弦理论的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一种镜像对称的泛化，被称为“（0,2）镜像对称”，这将是一个强大的计算工具，用于理解具有最小超对称性的四维理论，这些超对称性是通过在紧化空间上卷起或“紧化”六个维度而从弦理论中获得的。这项研究的一个重要部分将是进一步发展“量子束上同调”，这个概念最初是由夏普和谢尔登·卡茨教授提出的，它计算带电物质耦合的量子修正，并与这些理论的数学密切相关。该项目还将产生更广泛的重大影响。夏普教授将让研究生和博士后参与到他的研究中来，从而为刚开始研究这一领域的初级物理学家提供关键的培训。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.