Analytic Torsion on Calabi-Yau Moduli

University Of Iowa, Iowa City IA

Investigators

Abstract

Abstract Award: DMS-0606721 Principal Investigator: Hao Fang The principal investigator proposes to study analytic torsion on the Calabi-Yau manifolds. Inspired by Beshadsky-Coccoti-Ooguri-Vafa, the principal investigator , joint with Lu and Yoshikawa, has constructed a new holomorphic invariant of Calabi-Yau manifolds, which can be computed the invariant for one dimensional moduli spaces. In general, the principal investigator suggests an approach to analysis the asymptotic behavior of the new invariant, by using the local index theory techniques. This project should give insight on better understanding of the torsion invariants and the Calabi-Yau moduli. The proposed study can be viewed as an attempt to study problems in algebraic geometry using methods of differential geometry. By studying local geometry analytically near the singularities, the principal investigator also hopes to give new examples of the explicitly computable torsion invariants and reveal relations of torsion invariants to number theory. This project also will have broader impact. Torsion invariants have come from topology and high energy physics theories. The proposed study will shed new light on understanding Mirror Symmetry, which is one of the central problems in current theoretical physics. Understanding this theory will give mathematical foundation of the String Theory, which is a potential unified theory for high energy physics long sought after since Einstein's time. For example, the proposed research might lead to better understanding of (the number and the shape) of the universe. Interaction with fellow mathematicians and physicists is expected and will be necessary for the success of this research project. The principal investigator will participate the integrated research and education activities that will promote the education level of the nation.