Clifford Taubes

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Clifford Taubes (2010)

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

Live and act

Taubes grew up in Rochester , New York , studied at Cornell University and received his doctorate in 1980 under Arthur Jaffe at Harvard University ( The structure of static euclidean gauge fields ). He spent two years as a post-doc at the University of California, Berkeley . He has been Professor of Mathematics at Harvard since 1985, where he is now William Petschek Professor. His work on the mathematics of Yang Mills theories was important in Simon Donaldson's work on classifying differentiable structures on 4-manifolds(where there are exotic 4-manifolds with an infinite number of such structures), which essentially uses self-dual solutions of Yang-Mills equations and their modular spaces . He also worked on the new access to the Donaldson invariants of Edward Witten and Gromov-Witten invariant (he demonstrated the equivalence of 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 (1990). His PhD students include Tomasz Mrowka and Gregory Landweber.

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

Fonts

Books

  • with Arthur Jaffe : Vortices and Monopoles - structure of static gauge theories. Birkhäuser, 1980.
  • The Moduli Spaces on Four Manifold With Cylindrical Ends. Volume 1. Monographs in Geometry and Topology, 1993, ISBN 1-57146-007-1 .
  • Metrics, Connections and Gluing Theorems. CBMS Regional Conference Series in Mathematics. AMS, 1996, ISBN 0-8218-0323-9 .
  • Modeling Differential Equations in Biology. Prentice Hall, 2001. Cambridge University Press, 2008, ISBN 0-13-017325-8 .

Work

  • with Thomas Parker : On Witten's proof of the positive energy theorem. On: Comm. Math. Phys. 84, no. 2, 1982, pp. 223-238.
  • with Raoul Bott : On the rigidity theorems of Witten. On: J. Amer. Math. Soc. 2, No. 1, 1989, pp. 137-186.
  • Casson's invariant and gauge theory. In: J. Differential Geom. 31, No. 2, 1990, pp. 547-599.
  • The Seiberg-Witten invariants and symplectic forms. On: Math. Res. Lett. 1, No. 6, 1994, pp. 809-822.
  • with Guowu Meng : SW = Milnor torsion. In: Math. Res. Lett. 3, No. 5, 1996, pp. 661-674.
  • with John Morgan , Zoltán Szabó : A product formula for the Seiberg-Witten invariants and the generalized Thom conjecture. In: J. Differential Geom. 44, No. 4, 1996, pp. 706-788.
  • Counting pseudo-holomorphic submanifolds in dimension $ 4 $. In: J. Differential Geom. 44, No. 4, 1996, pp. 818-893.
  • SW-> GR: from the Seiberg-Witten equations to pseudo-holomorphic curves. In: J. Amer. Math. Soc. 9, No. 3, 1996, pp. 845-918.
  • GR-> SW: from pseudo-holomorphic curves to Seiberg-Witten solutions. On: J. Differential Geom. 51, No. 2, 1999, pp. 203-334.
  • GR = SW: counting curves and connections. In: J. Differential Geom. 52, No. 3, 1999, pp. 453-609.
  • with Curtis McMullen : 4-manifolds with inequivalent symplectic forms and 3-manifolds with inequivalent fibrations. In: Math. Res. Lett. 6, No. 5-6, 1999, pp. 681-696.
  • The Seiberg-Witten invariants and 4-manifolds with essential tori. In: Geom. Topol. 5, 2001, pp. 441-519
  • The Seiberg-Witten equations and the Weinstein conjecture. Part I in: Geom. Topol. 11, 2007, pp. 2117-2202. Part II in: Geom. Topol. 13, 2009, pp. 1337-1417.
  • Embedded contact homology and Seiberg-Witten Floer cohomology. In: Geom. Topol. 14, No. 5, 2010, pp. 2497-3000.
  • with Michael Hutchings : Proof of the Arnold chord conjecture in three dimensions 1. In: Math. Res. Lett. 18, No. 2, 2011, pp. 295-313.

literature

Web links

personal data
SURNAME Taubes, Clifford
ALTERNATIVE NAMES Taubes, Clifford Henry
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH February 21, 1954