The research interests of Dr. Boyadzhiev include: the comparison principle for systems of elliptic and parabolic differential equations; PDEs, including both cooperative, and non-cooperative systems; movement of waves in a solid body - in particular, the use of characteristics to track the path of seismic waves from an earthquake source to reception stations; development of methods for choosing the optimal solution of nonlinear vapor problem in mathematical modelling of Earth structure; deterministic models in geophysics and financial markets.