"A proof of Ore's Conjecture"
Abstract: A famous longstanding conjecture of Ore, posed in 1951, states that every element of a (nonabelian) finite simple group is a commutator. Partial results were obtained by many people. Very recently, in joint work with Liebeck, O'Brien and Tiep, we have proved the conjecture in full.
In the talk I will sketch the proof, which combines representation theory with a complicated induction, where the base for the induction is itself highly challenging; it required methods from computational group theory and 3 years of CPU time.