Joseph works in the School of Mathematical Sciences at Monash University as a Emeritus Professor

Joseph's research areas of interest are:

• The theory of particle methods for the numerical solution of fluid dynamics in astrophysics and geophysical fluid dynamics;
• star formation, relativistic fluid dynamics; volcanic eruptions and other multi-phase problems;
• waves breaking on beaches and similar free surface problems;
• fracture especially the dynamics of landslides, the calving of icebergs, and the collapse of magma chambers; the Mathematics of linked swimming bodies;
• geophysics and industry.