Joseph Malkoun

From the Berry-Robbins problem to the Atiyah-Sutcliffe conjectures and a Lie-theoretic generalization

Sir Michael Berry and Jonathan Robbins proposed an interesting approach in 1997 to explain the spin-statistics theorem which involves geometry and ordinary quantum mechanics, rather than quantum field theory. Related to this work is the Berry-Robbins problem, which was solved positively by Sir Michael Atiyah alone first, and then with Roger Bielawski using Nahm's equations.

There is a curious construction by Sir Michael Atiyah which is elementary and would be an actual solution to the Berry-Robbins problem provided a linear independence conjecture holds. Together with Paul Sutcliffe, this was refined into stronger conjectures involving the Atiyah-Sutcliffe determinant.

In this talk, I will introduce the Berry-Robbins problem and the Atiyah-Sutcliffe conjectures, and then briefly discuss my work which consists of a Lie-theoretic generalization of these conjectures. I will try to make this talk as accessible as possible, and hope to convince the audience that the Atiyah-Sutcliffe determinant is certainly worth studying!