Professor Thompson's primary area of research is the theory and measurement of fundamental constants such as the proton to electron mass ratio and the fine structure constant. He uses the measured constraints on the time variation of the constants to establish limits on the variation of basic physics parameters such as the Quantum Chromodynamic Scale, the Higgs Vacuum Expectation Value and the Yukawa couplings. A new area of research is using rolling scalar field beta functions to systematically characterize the wide range of alternative cosmologies and to establish the bounds on their parameter space imposed by the stability of the fundamental constants. Professor Thompson is the Principal Investigator for the Near Infrared Camera and Multi-Object Spectrometer, NICMOS on HST and has been active in using NICMOS on HST to do high redshift cosmology. He has measured the star formation history of the universe to redshift 6 and has determined the primary sources of the near infrared background and residual fluctuations. He is also working on designing a photonic lantern upgrade to the very high resolution spectrometer, PEPSI, on the Large Binocular Telescope.