##### Department of Mathematics,

University of California San Diego

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### Special Colloquium

## Hao Fang

#### Courant Institute, NYU

## Spectral invariants of torsion type and applications

##### Abstract:

R E C R U I T M E N T In this talk I will discuss some recent results on spectral invariants of torsion type. Spectral invariants of elliptic operators on compact manifolds are important global geometric quantities. The Ray-Singer torsion is a spectral invariant with significant topological implications. We discuss a new spectral invariant which generalizes Ray-Singer`s construction. This new invariant behaves nicely under holonomy restrictions. In particular, it coincides with the BCOV torsion (first constructed in Mirror Symmetry theory) when restricted to Calabi-Yau manifolds. As an application in algebraic geometry, we prove a Shafarevich type theorem for holomorphic moduli of polarized Calabi-Yau manifolds. We also show some links between our new invariant and automorphic forms, generalizing classical results in the two dimensional case. Parts of the results are joint work with Lu and Yoshikawa.

Host: Kate Okikiolu

### February 13, 2004

### 12:00 PM

### AP&M 6218

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