Nonlinear dynamics and chaos and its application, particularly to engineering systems.
Bifurcation theory, i.e. understanding abrupt changes from regular to complex dynamics. Application to rotor dynamics, aircraft bridges, flow-induced oscillation, parametric resonance in general including stabilisation 'upside down'.
The theory of how continuous enterties give rise to localised response. For example, solitary waves, localised buckling patterns and 'kinks' or dislocations in atomic lattices. A unifying mathematical description of such phenomena, and dedicated computational techniques.
Solitary waves in nonlinear optics. Localised pulses of light, so-called 'light bullets'.
The mechanics of rods, such as helical buckling of cables, pipelines and DNA strands.
Dynamics of piecewise systems, such as impacts, switches and backlash.
Very little experience: one live radio interview 10 years ago and phone interviews with journalists from New Scientist, Nature and EPSRC's Newsline in 2002