## Departmental Colloquium

Burt Totaro

UCLA/Cambridge

The integral Hodge conjecture for 3-folds

**Abstract:**The Hodge conjecture predicts which rational homology classes on a smooth complex projective variety can be represented by linear combinations of complex analytic subvarieties. In other words, it is about the difference between topology and complex analysis (or algebraic geometry). The integral Hodge conjecture, the analogous conjecture for integral homology classes, is false in general. We discuss negative results and some new positive results on the integral Hodge conjecture for 3-folds.

Friday November 16, 2012 at 3:00 PM in SEO 636