Anthony Joseph Tromba is an American mathematician, specializing in partial differential equations, differential geometry, and the calculus of variations.
Tromba received from Cornell University his bachelor's degree in 1965 and from Princeton University his M.S. in 1967 and his Ph.D. in 1968 under Stephen Smale with thesis Degree theory on Banach manifolds. Tromba was from 1968 to 1970 an assistant professor at Stanford University after which he joined the faculty of the University of California. From 1992-1995 he was Professor Ordinarius at the Ludwigs Maximilan University in Munich and is now currently distinguished professor at the University of California, Santa Cruz.
In 1975 he was a visiting scholar at the Institute for Advanced Study, in 1970 a visiting professor at the University of Pisa, and in 1974 a visiting professor at the University of Bonn and at SUNY. In 1975 he was a visiting professor at the University of Michigan, Ann Arbor and in 1986 he was an Invited Speaker of the ICM in Berkeley, California. In 1987 he led a research group at The Max Planck Institute in Bonn.
He is the author of eleven books.