| Citation | Kronheimer has made outstanding contributions to a number of areas, ranging from complex geometry to manifold topology. Much of his early work centred on "hyperkahler" structures in differential geometry, which are special solutions of the Einstein equations. Extending work of Hitchin, Kronheimer constructed and classified all asymptotically locally Euclidean hyperkahler manifolds, uncovering a beautiful and intricate theory which combines group theory, algebraic and differential geometry. Soon after, he discovered a family of hyperkahler structures on complex co-adjoint orbits. Since 1990, Kronheimer's work has been focused on 4-manifold topology. In a long collaboration with T.S. Mrowka he developed the theory of singular solutions of the Yang-Mills equations and applied it to obtain far-reaching results on 4-maifold invariants, and particularly to solve long-standing problems about surfaces in 4-manifolds. This work paved the way for the introduction of the Seiberg-Witten invariants, a development to which Kronheimer has made fundamental contributions. Kronheimer's achievements make him unquestionably one of the leading geometers in the world. |