This information is accurate as of the fellowship year indicated for each fellow.
Peter Kronheimer is the William Caspar Graustein Professor of Mathematics at Harvard University, where his research focuses on the interface between geometry and topology, particularly the topology of manifolds in low dimension.
During his fellowship at the Radcliffe Institute, Kronheimer is collaborating with Tomasz Mrowka (also a Radcliffe fellow this year) on a project that seeks to describe the subtle connections between two strands of research in the theory of knots in three-space: the quantum invariants of knots known as knot homology theories, and the study of knots and three-dimensional manifolds using techniques from gauge theory.
A fellow of the Royal Society, Kronheimer obtained his doctorate from the University of Oxford in 1987 and was a fellow of Merton College from 1989 to 1995. He and Mrowka were awarded the 2007 Oswald Veblen Prize in Geometry and the 2011 Joseph L. Doob Prize for their monograph Monopoles and Three-Manifolds (Cambridge University Press, 2007). Kronheimer earned his doctoral degree in mathematics from Oxford.