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.
