Robert Ernest Gompf (born 1957) is an American mathematician specializing in geometric topology.
Gompf received a Ph.D. in 1984 from the University of California, Berkeley under the supervision of Robion Kirby (An invariant for Casson handles, disks and knot concordants).
In 1990, he demonstrated with Tomasz Mrowka that there is a simply connected irreducible 4-manifold that admits no complex structures.
In 1995, he constructed new examples of simply connected compact symplectic 4-manifolds that are not homeomorphic or diffeomorphic to complex manifolds (Kähler manifolds).
[2] He was an invited speaker at the International Congress of Mathematicians in 1994 in Zurich (Smooth four-manifolds and symplectic topology).