Fields Geometric Analysis Colloquium

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.

https://www.fields.utoronto.ca/activities/26-27/geometric-analysis-colloquium