Analytic torsion and its applications

首席研究员计划继续研究解析扭转及其在微分几何和代数几何中的应用。他将研究关于Calabi-Yau模的BCOV猜想的高维版本。他还将学习扭转不变量的分析性质，重点是那些与极值度量问题有关的性质。这个项目将使我们深入了解扭转不变量的新结构，并更好地理解它在研究Calabi-Yau模和Yau-Tian-Donaldson猜想中的作用。扭转不变量已经出现在高能物理理论中，实际上是N=2超共形场论的重要组成部分。这项研究将为理解镜面对称性这一当前理论物理学中正在发展的分支提供新的线索。与数学家和物理学家同行的互动是预期的，也是这项研究项目成功所必需的。首席调查员积极参与本科生和研究生教育。他将继续鼓励更多的人，特别是妇女和少数民族，学习数学。他将参加将促进国家教育水平的综合研究和教育活动。

The principal investigator plans to continue his study of the analytic torsion and its application in differential and algebraic geometry. He will study the higher dimensional version of the BCOV conjecture on Calabi-Yau moduli. He will also study analytical properties of torsion invariants, with emphasis on those related to the extremal metric problems. This project should give insight on the new construction and better understanding of the torsion invariant and its role in the study of the Calabi-Yau moduli and the Yau-Tian-Donaldson conjecture.Torsion invariants have appeared in high energy physics theories and actually are crucial components of N=2 Super Conformal Field Theory. The proposed study will shed new light on understanding Mirror Symmetry, which is a developing branch in current theoretical physics. Interaction with fellow mathematicians and physicists is expected and will be necessary for the success of this research project. The principal investigator is actively engaged in undergraduate and graduate level education. He will continue to encourage more people, especially women and minorities, to study mathematics. He will participate in the integrated research and education activities that will promote the education level of the nation.