• Operator theory especially spectral theory of unbounded operators. Structural properties of bounded operators like compactness, norms, positivity among others. Applications of unbounded operators especially in the field of quantum mechanics and nanotechnology.

• Spectral Theory of Composites of Differential and Difference Operators (Funded by The World Academy of Science, TWAS). Phytochemistry, Textile and Renewable Energy, PTRE (Funded by World Bank). Mentoring African Research in Mathematics (Funded by LMS-MARM).