Colloquium: Voloch -- The ABC conjecture

The ABC conjecture is a simple, elementary statement about whole numbers and their prime
factorisations.  Nevertheless, it has numerous striking consequences.  Recently, S.
Mochizuki announced a proof of this conjecture, but its correctness is not yet fully
verified.  In this talk, I will state the conjecture, motivate it, explain some of its
consequences and try to explain the parts of Mochizuki’s strategy that I understand.