The Nahm transform is a remarkable construction relating solutions of different systems of differential equations which has appeared in many forms in gauge theory over the past 50 years. I will discuss work with Ákos Nagy implementing the transform from solutions of Nahm's ODEs to monopoles on Euclidean three-space with arbitrary symmetry breaking at infinity. I will describe some of the geometric analysis underlying the construction, involving families of Dirac-type operators, Fredholm theory, and model solutions used to recover the prescribed behaviour of the monopole at infinity.

Bio: Benoit Charbonneau is a professor of mathematics at the University of Waterloo. He works in geometric analysis and gauge theory, studying geometric PDEs and moduli spaces arising from monopoles, instantons, and related gauge-theoretic problems.