Kronheimer has frequently collaborated with Tomasz Mrowka from the Massachusetts Institute of Technology. Their collaboration began at the Mathematical Research Institute of Oberwolfach, and their first work developed analogues of Simon Donaldson's invariants for 4-manifolds with a distinguished surface. They used the tools developed to prove a conjecture of John Milnor, that the four-ball genus of a (p,q)-torus knot is (p-1)(q-1)/2. They then went on to develop these tools further and established a structure theorem for Donaldson's polynomial invariants using Kronheimer?Mrowka basic classes. After the arrival of Seiberg?Witten theory their work on embedded surfaces culminated in a proof of the Thom conjecture?which had been outstanding for several decades. Another of Kronheimer and Mrowka's results was a proof of the Pro
