David Gregory Ebin (born 24 October 1942, Los Angeles)^[1] is an American mathematician, specializing in differential geometry.

Ebin received in 1964 from Harvard University his bachelor's degree and in 1967 his Ph.D. from Massachusetts Institute of Technology under Isadore Singer with thesis On the space of Riemannian metrics.^[2] From 1968 to 1969 Ebin was a lecturer at the University of California, Berkeley. He became in 1969 an associate professor and in 1978 a full professor at the Stony Brook University.

Ebin in the academic years 1983–1984 and 1991–1992 was a visiting professor at UCLA, in 1971 a docent at the École Polytechnique and the University of Paris VII, and in 1976 a member of the Courant Institute in New York. He was elected a Fellow of the American Mathematical Society in 2012.

His research deals with differential geometry, infinite-dimensional manifolds (in hydrodynamics and in his treatment of the space of Riemannian metrics), nonlinear partial differential equations, mathematical hydrodynamics (including slightly compressible fluids), and elastodynamics. He investigated in his dissertation the space of Riemannian metrics on a compact manifold and gave this infinite-dimensional space a Riemannian structure.

In 1970 he was, with Jerrold Marsden, an Invited Speaker with talk On the motion of incompressible fluids at the ICM in Nice.

Ebin is since 1971 married to Barbara Jean Ebin and has four children.