Christian Okonek

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Christian Okonek, Berkeley 1981

Christian Okonek (* 1952 in Göttingen ) is a German mathematician who deals with algebraic and complex geometry. He is a professor at the University of Zurich .

Life

Okonek studied mathematics at the University of Göttingen from 1973 to 1978 and received his doctorate there in 1980 under Tammo tom Dieck (algebraic investigations on equivariate unitary cobordism theory) and completed his habilitation in 1982. He was a Heisenberg fellow for research stays at the University of California, Berkeley , at noon -Leffler Institute and at the Max Planck Institute for Mathematics in Bonn . From 1989 to 1992 he was a professor at the University of Bonn and then a full professor at the University of Zurich.

He is particularly concerned with vector bundles on algebraic surfaces and complex projective varieties and their topology. Including questions of the existence of different differentiable structures and applications of the mathematics of gauge theories (instantons, Donaldson, Floer and Seiberg / Witten invariants, etc.) to algebraic surfaces. After Simon Donaldson with had given an example of a 4-manifold with two differentiable structures showed Okonek and van de Ven (and independent John Morgan and Robert Friedman ) that there are infinitely many differentiable structures on this space.

His doctoral students include Professors Andrei Teleman, Alexander Schmitt and Manfred Lehn.

Fonts (selection)

  • with Michael Schneider , Heinz Spindler: Vector bundles on complex projective space, Birkhäuser 1980, new edition 2011 (with appendix by S I. Gelfand)
  • Barth-Lefschetz theorems for singular spaces, J. Reine Angew. Math., Vol. 374, 1987, pp. 24-38
  • with Antonius van de Ven : Stable bundles and differentiable structures on certain elliptic surfaces, Inventiones Mathematicae, Volume 86, 1986, pp. 357-370
  • with Antonius van de Ven: Stable bundles, instantons and -structures on algebraic surfaces, in: Several complex variables VI, Encyclopedia of Mathematical Sciences, Springer, 1990
  • Instanton invariants and algebraic surfaces, in; Geometric topology: recent developments (Montecacini Terme 1990), Lecture notes in mathematics 1504, Springer 1991, pp. 138-186
  • with Wolfgang Ebeling : Donaldson invariants, monodromy and singularities, Intern. J. Math. Vol. 1, 1990, pp. 233-250
  • with W. Ebeling: On the diffeomorphism groups of certain algebraic surfaces, L'Enseignement Mathematique, Volume 37, 1991, pp. 249-262
  • Donaldson-Floer invariants and singularities, in: Geometry of complex projective Varieties (Cetraro 1990), Seminar Conf. 9, Mediterranean, Rende 1993, pp. 203-217
  • The Fourth Dimension, Elements of Mathematics, Volume 50, 1995, pp. 107-115
  • with A. Teleman: Quaternionic monopoles, Comm. Math. Phys., Vol. 180, 1996, pp. 363-388
  • with A. Teleman: Recent developments in Seiberg-Witten theory and complex geometry, in: Several complex variables (Berkeley 1995–1996), MSRI Publ. 37, Cambridge UP 1999
  • with A. Teleman: Gauge theoretic equivariant Gromov-Witten invariants and the full Seiberg-Witten invariants of ruled surfaces, Comm. Math. Phys., Vol. 227, 2002, pp. 551-585

Web links

Individual evidence

  1. ↑ Christian Okonek in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ↑ Biography of his essay The Fourth Dimension in Elements of Mathematics, 1995.
  3. ^ Okonek, The Fourth Dimension, Elements of Mathematics 1995
  4. ↑ Based on his inaugural address at the University of Zurich in 1994
personal data
SURNAME Okonek, Christian
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH 1952
PLACE OF BIRTH Goettingen