##### Department of Mathematics,

University of California San Diego

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### Final Defense

## Jonathan Conder

#### UCSD

## Geometric links between $E_6$ and theta divisors

##### Abstract:

The interesting part of the cohomology of the theta divisor $D$ of an abelian fivefold $A$ shares numerical properties with the Lie algebra $E_6$. We define 27 surfaces inside $D$, one for each realisation of $A$ as a Prym variety, and explain how they generate a sublattice of $H^4(D, \mathbb{Z})$ isomorphic to the root lattice of $E_6$. This gives an effective proof of the Hodge conjecture for the theta divisor.

Advisor: Elham Izadi

### May 30, 2019

### 9:30 AM

### AP&M 6218

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