Applied and computational mathematics, in two distinct research tracts: (1) the application of statistical physics ideas, data sciences, and dynamics on probability distributions, to the understanding complex non-equilibrium physical and human systems and to the development of forecasting tools for these systems; (2) the role of ocean and ocean transport in climate dynamics and in nearshore processes. Example research problems in tract 1: resilience and uncertainty quantification in natural and human complex systems, using data and physical models. Adaptive time series methods for climate and financial data. Extreme/rare events. Dimension and uncertainty reduction in complex systems. Example research problems in tract 2: oil spill dynamics, wave breaking dynamics, wave-generated transport, the role of oceans in global climate. Sediment dynamics. Outside of these tracts he has also done research on wavelets, bone dynamics, blood cell dynamics, public choice and elections, solitary waves, high performance computing.