In a series of four long papers in the 1990s (collected in ), Taubes proved that, on a closed
symplectic four-manifold, the (gauge-theoretic)
Seiberg–Witten invariant is equal to an invariant which enumerates certain
pseudoholomorphic curves and is now known as
Taubes's Gromov invariant. This fact improved mathematicians' understanding of the topology of symplectic four-manifolds. More recently (in ), by using Seiberg–Witten
Floer homology as developed by
Peter Kronheimer and
Tomasz Mrowka together with some new estimates on the spectral flow of
Dirac operators and some methods from , Taubes proved the longstanding
Weinstein conjecture for all three-dimensional
contact manifolds, thus establishing that the Reeb vector field on such a manifold always has a closed orbit. Expanding both on this and on the equivalence of the Seiberg–Witten and Gromov invariants, Taubes has also proven (in a long series of preprints, beginning with ) that a contact 3-manifold's embedded contact homology is isomorphic to a version of its Seiberg–Witten Floer cohomology. More recently, Taubes, C. Kutluhan and Y-J. Lee proved that Seiberg–Witten Floer homology is isomorphic to Heegaard Floer homology. ==Honors and awards==