Symmetric differentials and the fundamental group -- Burt Totaro, April 20, 2012

Consider a smooth complex projective variety X. Hodge theory shows that sections of exterior powers of the cotangent bundle are related to the topology of X. What about symmetric powers of the cotangent bundle? We discuss the relation between the topology of X and its "symmetric differentials". One interest of these results is that symmetric differentials give information in the direction of "Kobayashi hyperbolicity"; for example, they limit how many rational curves X can contain.