# Weitere Informationen zum ausgewählten Vortrag

## Elliptic Genera and $G_2$-manifolds

### Jonas Lenthe

#### Monday, 2021-11-29 16:15

In 1988 Witten showed that the universal elliptic genus of a manifold $M$ can be interpreted as the index of a twisted Dirac operator on the the loop space of $M$. Furthermore he discovered, that the index of this Dirac operator has similar modular properties, if one restricts to string manifolds. The resulting modular form is now called the Witten genus.

In my talk I will give an introduction to modular forms and I will formaly derive the Witten genus from the index theorem.

If we compare the Witten genus with the elliptic genus in dimension $8$, there occur characteristic classes, which are connected with the Nu-invariant of $G_2$-manifolds.