##### Department of Mathematics,

University of California San Diego

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### UCI-UCR-UCSD Southern California Differential Geometry Seminar

## Guangbo Xu

#### SUNY Stony Brook

## Bershadsky--Cecotti--Ooguri--Vafa torsion in Landau--Ginzburg models

##### Abstract:

In the celebrated work of Bershadsky--Cecotti--Ooguri--Vafa the genus one string partition function in the B-model is identified with certain analytic torsion of the Hodge Laplacian on a K$\ddot{\text{a}}$hler manifold. In a joint work with Shu Shen (IMJ-PRG) and Jianqing Yu (USTC) we study the analogous torsion in Landau--Ginzburg models. I will explain the corresponding index theorem based on the asymptotic expansion of the heat kernel of the Schr$\ddot{\text{o}}$dinger operator. I will also explain the rigorous definition of the BCOV torsion for homogeneous polynomials on ${\mathbb C}^N$. Lastly I will explain the conjecture stating that in the Calabi--Yau case the BCOV torsion solves the holomorphic anomaly equation for marginal deformations.

### October 9, 2018

### 3:00 PM

### UCI - Rowland Hall 306

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