Number Theory Seminar

Tuesday, Oct. 28
David McKinnon, University of Waterloo
K3 surfaces, rational curves, and rational points

ABSTRACT:

In 1981, Bogomolov conjectured that every rational point on a K3 surface lies on a rational curve. Twenty-eight years later, this conjecture is widely believed to be untrue, and so the hunt is on to find rational points that don't lie on any rational curves. In this talk, I will outline some strategies for finding counterexamples to Bogomolov's conjecture, and explain the extent to which they have been successful.