# The Integral Hodge Conjecture For 3-Folds

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Burt Totaro, DPMMS, Cambridge University
Fine Hall 322

The Hodge conjecture predicts which rational homology classes on a smooth complex projective variety can be represented by linear combinations of complex subvarieties. In other words, it is about the difference between topology and 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.