Lyle Hoffman's research is in the field of radioastronomy and cosmology. He travels to Arecibo Observatory, the 305m radio telescope in Puerto Rico at least once a year, taking a student assistant each time. He also makes use of the Very Large Array in New Mexico. The data acquired at these observatories allow him to investigate the internal structure and dynamics of individual dwarf and spiral galaxies; the motions of these galaxies about the Local Supercluster of galaxies; and the effects of the galaxies' environment on their gas content and evolution.
Lyle uses the workstation in his office heavily for detailed analysis of the data he brings back from the radiotelescopes. He is currently a member of the ALFALFA consortium conducting a large-scale survey of neutral hydrogen in the local universe whether or not there are visible stars embedded in the gas. Lyle's work has been supported by grants from the National Science Foundation, and he maintains collaborations with astronomers at Cornell University, Queen's University in Ontario and Tel Aviv University along with those at Arecibo. In the recent past, he has supervised student research and honors theses in numerical simulation of galaxy groups, in analysis of neutral hydrogen data for dwarf galaxies, and in the acoustics of the human vocal tract. Students have been named as coauthors on several recent publications of Arecibo data. Peiyuan Mao '11 (shown at the Undergraduate ALFALFA Team workstation in HSC 036) worked with Lyle during the summers 2008 and 2009 on clusters of galaxies at the outer edge of the ALFALFA survey and on Active Galactic Nuclei identified by neutral hydrogen absorption signatures.