Tutte seminar - Kevin Purbhoo

The 012-Puzzle Conjecture

Abstract:

The 012-Puzzle conjecture in algebraic combinatorics was formulated by A. Knutson about 10 years ago. The statement is quite elementary and easy to understand. It is also a bit surprising and hard to believe. Nevertheless, extensive computer experiments seemed to bear out the idea that the conjecture could be true, and for several years this was all that was known.

Shortly after the conjecture was publicized, A. Buch, A. Kresch, and H. Tamvakis came up with a strategy for proving it. Unfortunately, it didn't quite work: one of the key lemmas turned out to be false. We now know how to replace this lemma by one that is true, and thereby complete the proof.

The main purpose of this talk will be to show lots of pictures. Secondary considerations will be to explain the statement of the conjecture, the context in which it arises, and the main ideas of the proof.