Clifford Taubes
Clifford Henry Taubes (born February 21, 1954) is the William Petschek Professor of Mathematics at Harvard University and works in gauge field theory, differential geometry, and low-dimensional topology. His brother is the journalist Gary Taubes. Early career. Taubes received his Ph.D. in physics in 1980 under the direction of Arthur Jaffe, having proven results collected in about the existence of solutions to the Landau–Ginzburg vortex equations and the Bogomol'nyi monopole equations. Soon, he began applying his gauge-theoretic expertise to pure mathematics. His work on the boundary of the moduli space of solutions to the Yang -Mills equations was used by Simon Donaldson in his proof of Donaldson's theorem. He proved in that R has an uncountable number of smooth structures (see also exotic R), and (with Raoul Bott in ) proved Witten's rigidity theorem on the elliptic genus. Work based on Seiberg–Witten theory. 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 has transformed  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 embedded contact homology is isomorphic to Heegaard Floer homology.