Rational curves on K3 surfaces
Brendan Hassett, Rice

More than two decades ago, Bogomolov and Mori-Mukai showed that general K3 surfaces admit infinitely many rational curves. However, their argument says little about any particular K3 surface. The main result of this talk is that every K3 surface with Picard group generated by a divisor of degree two has infinitely many rational curves. (joint work with Bogomolov and Tschinkel)