Geha grew up wanting to be an astronaut after seeing the launch of the first Space Shuttle, and shifted her interests to astronomy in high school as a more realistic career path.[5] She majored in applied and engineering physics as an undergraduate at Cornell University, graduating with a bachelor's degree in 1995. She earned a master's degree in astronomy in 1998 from New Mexico State University,[4] but, dissatisfied with the program, left before completing a Ph.D. After a brief stint at the Lawrence Berkeley National Laboratory, she reapplied to graduate schools,[2] and went to the University of California, Santa Cruz for a Ph.D., which she completed in 2003.[4] Her dissertation, Internal dynamics, structure and formation of dwarf elliptical galaxies, was jointly supervised by Puragra (Raja) GuhaThakurta and Roeland van der Marel.[6]
She has been director of Yale Telescope Resources since 2012.[4] In 2017, she was given a Howard Hughes Medical Institute professorship, funding a five-year program for science education of military veterans.[7]