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

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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.