Gert Heckman

from Wikipedia, the free encyclopedia
Gert Heckman, Oberwolfach 2008

Gerrit Jacobus "Gert" Heckman (* 1953 ) is a Dutch mathematician.

Heckman received his doctorate in 1980 under Gerrit van Dijk (and Johannes Jisse Duistermaat ) at the University of Leiden with a dissertation in which Alexander Kirillov's orbit method was applied to compact Lie groups for the asymptotic description of branching rules, i.e. the behavior of representations with restriction to subgroups (Projections of Orbits and Asymptotic Behavior of Multiplicities for Compact Lie Groups). When he returned in 1982 he became Gerrit van Dijk's assistant. He is a professor at Radboud University Nijmegen .

He deals with representation theory, hypergeometric functions, symplectic geometry, hyperbolic geometry and mathematical physics (integrable systems). Hypergeometric functions associated with the root systems of Lie algebras (Heckman-Opdam Hypergeometric Functions) are named after him and Eric Opdam , and the Duistermaat-Heckman formula (1982) in symplectic geometry is named after him and Johannes Jisse Duistermaat .

He also dealt with representations of the derivation of Kepler's laws in schools. He also came to a new appreciation of the original derivation by Isaac Newton .

He is co-editor of Indagationes Mathematicae.

Fonts (selection)

  • Projections of Orbits and Asymptotic Behavior of Multiplicities for Compact Connected Lie Groups, Invent. Math., Vol. 67, 1982, pp. 333-356
  • with JJ Duistermaat: On the variation in the Cohomology of the Symplectic Form on the Reduced Phase Space, Invent. Math., Vol. 69, 1982, pp. 259-268. Addendum, Vol. 72, 1983, pp. 153-158.
  • with Eric Opdam: Root systems and hypergeometric functions I, Compositio Mathematica, Volume 64, 1987, pp. 329-352. Part 2 of Heckman, Compositio Mathematica, Volume 64, 1987, pp. 353-373
  • with Michel Duflo , Michele Vergne : Projection d'orbites, formule de Kirillov et formule de Blattner, Mém. Soc. Math. France (NS) 15: 65-128 (1984).
  • with Frits Beukers, W. Dale Brownawell: Siegel Normality, Annals of Mathematics, Volume 127, 1988, pp. 279-308.
  • with Frits Beukers : Monodromy for the generalized hypergeometric function of Thomae, Invent. math., Vol. 95, 1989, pp. 325-354.
  • Hecke algebras and hypergeometric functions, Invent. Math., Vol. 100, 1990, pp. 403-417.
  • An elementary approach to the hypergeometric shift operators of Opdam, Invent. Math., Vol. 103, 1991, pp. 341-350.
  • with Eric Opdam: Harmonic analysis for affine Hecke algebra, in: Current developments in Mathematics 1996, Intern. Press 1997, pp. 37-60.
  • with Eric Opdam : Yang's system of particles and Hecke algebras, Annals of Mathematics, Volume 145, 1997, pp. 139-173.
  • Quantum integrability of the Kovalevsky top, Indag. Math. NS 9 (1998), 223-246.
  • Dunkl Operators, Seminaire Bourbaki 828, 1997
  • with Eduard Looijenga : The moduli space of rational elliptic surfaces, in: Algebraic Geometry 2000, Azumino, Advanced Studies in Pure Mathematics 36 (2002), pp. 185–248.
  • with Wim Couwenberg, Eduard Looijenga: On the geometry of the Calogero-Moser system, Indag. Math., NS, 16: 443-459 (2005).
  • with Wim Couwenberg, Eduard Looijenga: Geometric structures on the complement of a projective arrangement, Publications mathematiques de l'IHES 101 (2005), 69–161.
  • with Tim de Laat: On the Regularization of the Kepler Problem, Journal of Symplectic Geometry, Volume 10, 2012, pp. 463-473.
  • with Eduard Looijenga: Hyperbolic Structures and Root Systems, in: Casimir Force Casimir Operators and the Riemann Hypothesis, de Gruyter, 2010, pp. 211–228.
  • Sander Rieken: An Odd Presentation for W (E6), in: K3 Surfaces and Their Moduli, Proceedings of the Schiermonnikoog Conference 2014, Birkhäuser, Progress in Math. 315, 2016, pp. 97–110 (Weyl group of the exceptional Lie group E6)
  • with Sander Rieken: Hyperbolic Geometry and Moduli of Real Curves of Genus Three, Math. Annalen

Web links

Individual evidence

  1. ^ Heckman, Recollections of Hans Duistermaat (pdf)
  2. ↑ Gert Heckman in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  3. ↑ Maris van Haandel, Gert Heckman: Teaching the Kepler Laws for Freshmen, The Mathematical Intelligencer, Volume 31, Issue 2, 2009, pp 40-44.
personal data
SURNAME Heckman, Gert
ALTERNATIVE NAMES Heckman, Gerrit Jacobus
BRIEF DESCRIPTION Dutch mathematician
DATE OF BIRTH 1953