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Calabi-Yau模的BCOV猜想的高维版本。他还将研究扭转不变量的解析性质，重点是那些与极值度量问题有关的性质。该项目将对新的构造和更好地理解扭转不变量及其在Calabi-Yau模和you - tian - donaldson猜想研究中的作用提供见解。扭转不变量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。该研究将为理解镜像对称提供新的思路，这是当前理论物理学的一个发展分支。期望与其他数学家和物理学家进行互动，这对于本研究项目的成功是必要的。首席研究员积极从事本科和研究生水平的教育。他将继续鼓励更多的人，尤其是女性和少数民族，学习数学。他将参与提高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.