##### Department of Mathematics,

University of California San Diego

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### Geometry Topology

## Mohammed Abouzaid

#### University of Chicago

## Homological mirror symmetry for toric varieties

##### Abstract:

I will begin by explaining the statement of the Homological Mirror Symmetry conjecture for Fano toric varieties and outline how Lefschetz fibrations have been used to prove the conjecture in some cases. I will then show how Mikhalkin's flavour of tropical geometry can be used to prove half of the homological mirror conjecture for all smooth projective toric varieties (dropping the Fano condition!).

Host: Mark Gross

### January 10, 2007

### 2:00 PM

### AP&M 7218

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