Robert Ernest Gompf is an American mathematician specializing in geometric topology.
Gompf received a Doctor of Philosophy in 1984 from the University of California, Berkeley under the supervision of Robion Kirby (On invariant for Casson handles, disks and knot concordants).
He is now a professor at the University of Texas at Austin. His research concerns the topology of 4-manifolds. In 1995 he constructed new examples of simply connected compact symplectic 4-manifolds that are not homeomorphic or diffeomorphic to complex manifolds (Kähler manifolds).
He is a fellow of the American Mathematical Society.
He was an invited speaker at the International Congress of Mathematicians in 1994 in Zurich (Smooth four-manifolds and symplectic topology).