Claude LeBrun

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Claude LeBrun at Oberwolfach, 2012.jpeg

Claude R. LeBrun (born November 26, 1956 ) is a mathematician who deals in particular with four-dimensional manifolds and especially Einsteinian manifolds , using techniques of differential geometry, differential topology, complex geometry, symplectic and algebraic geometry.

LeBrun received his PhD in 1980 from Roger Penrose at Oxford University ( Spaces of complex geodesics and related structures ). He is a professor at the State University of New York at Stony Brook (SUNY).

After John A. Thorpe and Nigel Hitchin specified a necessary condition for the existence of Einstein metrics on four-dimensional compact smooth manifolds in the form of an inequality named after them between topological invariants, LeBrun and independently Andrea Sambusetti showed that the condition is not sufficient. They showed the existence of an infinite number of non-homeomorphic manifolds that satisfy the inequality but do not allow an Einstein metric.

With Fabrizio Catanese , he proved the existence of smooth, compact -dimensional manifolds with two Einstein metrics whose scalar curvatures have opposite signs, thereby refuting a conjecture by Arthur Besse .

In 1994 he was invited speaker at the International Congress of Mathematicians in Zurich (Anti Self-Dual Metrics and Kähler-Geometry). He is a fellow of the American Mathematical Society .

Fonts

  • Editor Essays on Einstein manifolds: lectures on geometry and topology , International Press, Cambridge / Massachusetts 1999
  • Einstein metrics on complex surfaces , in Geometry and physics (Aarhus, 1995) , Lecture Notes in Pure and Appl. Math., Vol. 184, Dekker, New York, 1997, pp. 167-176
  • Twistors for tourists: a pocket guide for algebraic geometers , Algebraic geometry — Santa Cruz 1995, Proc. Sympos. Pure Math., Vol. 62, Amer. Math. Soc., Providence, RI, 1997, pp. 361-385
  • Twistors, Kähler manifolds, and bimeromorphic geometry , part 1, 2, J. Amer. Math. Soc. 5 (1992), pp. 289-316, pp. 317-325
  • Counter-Examples to the Generalized Positive Action Conjecture , Comm. Math. Phys. 118 (1988) 591-596 (refutation of the generalized Positive Action Conjecture by Stephen Hawking and Pope)

Web links

Individual evidence

  1. ^ Mathematics Genealogy Project
  2. ↑ LeBrun Four-manifolds without Einstein Metrics , Math. Res. Letters 3 (1996), pp. 133--147
  3. ↑ Sambusetti An obstruction to the existence of Einstein metrics on 4-manifolds , CR Acad. Sci. Paris 322 (1996), pp. 1213-1218
  4. ↑ LeBrun, Catanese On the scalar curvature of Einstein manifolds , Math. Res. Lett. 4, No. 6 (1997), 843-854
personal data
SURNAME LeBrun, Claude
ALTERNATIVE NAMES LeBrun, Claude R.
BRIEF DESCRIPTION mathematician
DATE OF BIRTH November 26, 1956