Reid, together with the Fields Medallist Mori in Japan, initiated the most important developments in the geometry of algebraic 3-folds in the last thirty years, through his study of the singularities necessarily appearing on minimal models of 3-folds. His work and current interests are described under the heading of Algebraic Geometry elsewhere on this web-page.

Mond works primarily on singularities of mappings rather than of varieties. His research has focussed on analogues of the Milnor fibre of a hypersurface singularity, viewed as the stable approximation to the unstable singularity. This has led to the study of the topology of images and discriminants of stable perturbations of unstable maps, some of which may be seen in the pictures below, which are taken from a paper shortly to appear in Compositio Mathematica.

Via Augmentation and Concantentation, the double point and the cusp generate all codimension 1 singularities of maps from surfaces to 3 space (whose good real stable perturbations are shown in the last row)

Image of good real perturbation of binary concatenation of two cusps

Current interests include free and almost free divisors, real versus complex in singularity theory, Frobenius manifolds and applications of Morse theory to Statistics (the topology of the space of explanations).

Current Research Students: Ignacio de Gregorio, Alvaro Pelayo