Dr. Alexander's main area of interest is the study of the dynamic solar corona via the analysis and theoretical interpretation of thermal and non-thermal radiation. His primary contributions have been in the area of solar flare and CME physics where he has developed theoretical models for the production of gamma-rays, hard X-rays, and soft X-ray line broadening. He is involved with a number of projects relating to understanding theinitiation and evolution of solar flares and CMEs by exploring particle production in association with, magnetic topology, helicity injection and filament eruptions.  He currently leads the NSF-funded INSPIRE project to study the magnetic interactions between stars and planets and is devising a novel snapshot hyperspectral imager for Earth remote sensins with colleagues in bioengineering. He is author of "The Sun" (2009) by Greenwood Press.