Citation | Joyce has made remarkable and seminal contributions to Differential Geometry: many of his results also have a strong bearing on current developments in Theoretical Physics. In early work he found a number of ingenious constructions of manifolds with special structures, often related to the quaternions. His most renowned achievements are probably his proofs of the existence of compact manifolds with exceptional holonomy groups. These involve a marvellous blend of geometry and analysis, and the results have opened up an entirely new field. More recently, Joyce has developed a many-faceted theory of singularities of Special Lagrangian submanifolds in Calabi-Yau manifolds. |