Clifford Taubes

Clifford Henry Taubes ( born February 21, 1954) is an American mathematician, with differential geometry, topology, and mathematical physics ( gauge theories ) employed.

Life and work

Taubes grew up in Rochester, New York, graduated from Cornell University and his doctorate in 1980 at Arthur Jaffe at Harvard University ( The structure of static euclidean gauge fields ). As a post-doc, he spent two years at the University of California, Berkeley. He is since 1985 professor of mathematics at Harvard, where he is William Petschek Professor today. His work on the mathematics of Yang-Mills theories were important in Simon Donaldson's work on the classification of differentiable structures on 4 -manifolds (where there are exotic 4 -manifolds with infinitely many such structures ), which essentially self -dual solutions of Yang - Mills equations and their moduli spaces used. He also worked on the new access to the Donaldson invariants of Edward Witten and Gromov -Witten invariant ( he proved the equivalence of the Seiberg - Witten and Gromov invariants for symplectic 4 -manifolds ).

Taubes is a member of the National Academy of Sciences (1996 ) and the American Academy of Arts and Sciences. His doctoral include Tomasz Mrowka and Gregory Landweber.

Taubes in 1991 received the Oswald Veblen - Prize of the American Mathematical Society and in 1993 the Elie Cartan Prize of the French Mathematical Society. In 1999 he was Bowen Lecturer at Berkeley. In 2008 he was awarded the Clay Research Award for his proof of the Weinstein conjecture in three dimensions ( existence of closed orbits of the Reeb vector fields in closed contact manifolds ). Taubes in 2008 was awarded the NAS Award in Mathematics. In 2009 he was awarded the Shaw Prize for mathematics awarded jointly with Simon Donaldson. In 1986 he was invited speaker at the ICM, Berkeley ( gauge theories and nonlinear partial differential equations ) and in Berlin in 1998 (The geometry of the Seiberg -Witten Invariants ). In 1994 he gave a plenary lecture at the ICM in Zurich ( anti- self- dual geometry ).

Writings

  • Modeling Differential Equations in Biology, Prentice Hall, 2001, Cambridge University Press, 2008, ISBN 0-13-017325-8
  • The moduli spaces on Four Manifolds With Cylindrical Ends, Vol.1, Monographs in Geometry and Topology, 1993, ISBN 1-57146-007-1
  • Metrics, Connections and Gluing theorem, CBMS Regional Conference Series in Mathematics, AMS, 1996, ISBN 0-8218-0323-9
  • With Arthur Jaffe: Vortices and monopole - structure of static gauge theories, Birkhauser, 1980

Works ( selection)

  • With Hutchings: Proof of the Arnold chord conjecture in three dimensions 1 Math Res Lett. 18 (2011 ), no 2, 295-313.
  • Embedded contact homology and Seiberg - Witten Floer cohomology I, II, III, IV, V ( Geom Topol. 14 (2010 ), no 5, 2497-3000 )
  • The Seiberg - Witten equations and the Weinstein conjecture. I ( Geom Topol. 11 ​​(2007), 2117-2202 ), II ( Geom Topol. 13 (2009 ), no 3, 1337-1417 )
  • The Seiberg - Witten invariants and 4- manifolds with essential tori. Geom Topol. 5 (2001), 441-519
  • With McMullen: 4 - manifolds with inequivalent symplectic forms and 3- manifolds with inequivalent fibrations. Math Res Lett. 6 (1999 ), no 5-6, 681-696.
  • GR = SW: counting curves and connections. J. Differential Geom 52 (1999 ), no 3, 453-609.
  • GR- > SW: from pseudo- holomorphic curves to Seiberg - Witten solutions. J. Differential Geom 51 (1999 ), no 2, 203-334.
  • SW > GR: from the Seiberg - Witten equations to pseudo- holomorphic curves. J. Amer. Math Soc. 9 (1996 ), no 3, 845-918.
  • Counting pseudo- holomorphic submanifolds in dimension $ 4 $. J. Differential Geom 44 (1996 ), no 4, 818-893.
  • Conjecture A product formula for the Seiberg - Witten invariants and the generalized Thom: Morgan, Szabó. J. Differential Geom 44 (1996 ), no 4, 706-788.
  • With Meng: SW = Milnor torsion. Math Res Lett. 3 (1996 ), no 5, 661-674
  • The Seiberg - Witten invariants and symplectic forms. Math Res Lett. 1 (1994 ), no 6, 809-822.
  • Casson 's invariant and gauge theory. J. Differential Geom 31 (1990 ), no 2, 547-599
  • With Bott: On the rigidity theorems of Witten. J. Amer. Math Soc. 2 (1989 ), no 1, 137-186.
  • Parker: On Witten 's proof of the positive energy theorem. Comm. Math Phys. 84 (1982 ), no 2, 223-238.
Gromov–Witten invariant Oswald Veblen Prize in Geometry Alan Weinstein Berkeley, California Curtis T. McMullen John Morgan (mathematician) Raoul Bott Integrated Authority File
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