Gert Heckman

With my wife Kitty in the mountains of Lazio, 2010

Research interests:

Representation theory
Symplectic geometry
Hyperbolic geometry
Group theory
Hypergeometric functions
Integrable systems

Editorial board:

Indagationes Mathematicae

How to contact me:

Gert Heckman
Department of Mathematics
P.O. Box 9010
6500 GL Nijmegen
The Netherlands

phone: +31 24 3653233
fax: +31 24 3652140
office: Huygens Building, HG 03.737
address: Heyendaalseweg 135, 6525 AJ Nijmegen

e-mail: G.Heckman"at"math.ru.nl


Publications:

On a bike ride in Tuscany under a famous "Sleepwalker" street sign, 2010

Jesse J. Heckman, Rémi Proville, Gert J. Heckman, Alireza Azarfar, Tansu Celikel and Bernhard Englitz:
High-precision spatial localization of mouse vocalizations during social interaction,

Scientific Reports, June 2017.

Gert Heckman and Sander Rieken:
Hyperbolic Geometry and Moduli of Real Curves of Genus Three,

Math. Annalen, to appear.

Gert Heckman and Lei Zhao:
Angular Momenta of Relative Equilibrium Motions and Real Moment Map Geometry

Invent. Math. 205 (2016), 671–691.

Gert Heckman and Eric Opdam:
Jacobi Polynomials and Hypergeometric Functions associated with Root Systems

Preprint September 2017. This will be Chapter 8 of Volume 5 (Multivariable Special Functions)
of the new Askey-Bateman project, edited by Tom Koornwinder and Jasper Stokman.

Gert Heckman and Sander Rieken:
Two Lorentzian Lattices

Preprint December 8, 2014.
The first sentence on page 19 in incorrect, as I overlooked the possibility
of codimension 2 intersections of the mirrors with the real form. Therefore
additional work is needed, and for the moment Theorem 5.2 is not yet proved.

Gert Heckman and Sander Rieken:
An Odd Presentation for W(E6)

In: K3 Surfaces and Their Moduli, Progress in Math. 315 (2016), 97-110,
Proceedings of the Schiermonnikoog Conference 2014, Birkhäuser.

Gert Heckman and Maarten van Pruijssen:
Matrix Valued Orthogonal Polynomials for Gelfand Pairs of Rank One

Tohoku Mathematical Journal, 68:3 (2016).

Gert Heckman:
The Allcock Ball Quotient

Pure and Applied Mathematics Quarterly, 11:4 (2015), 655–681.

Gert Heckman and Tim de Laat:
On the Regularization of the Kepler Problem

Journal of Symplectic Geometry, 10:3 (2012), 463-473.

Gert Heckman and Eduard Looijenga:
Hyperbolic Structures and Root Systems
Casimir Force Casimir Operators and the Riemann Hypothesis, de Gruyter (2010), 211-228.

The "Duistermaat-Heckman" formula on the wall of the Hans Duistermaat room, Utrecht, 2015

Maris van Haandel and Gert Heckman:
Teaching the Kepler Laws for Freshmen

The Mathematical Intelligencer 31:2 (2009),40-44.

Wim Couwenberg, Gert Heckman and Eduard Looijenga:
On the geometry of the Calogero-Moser system

Indag. Math., N.S., 16 (2005), 443-459.

Wim Couwenberg, Gert Heckman and Eduard Looijenga:
Geometric structures on the complement of a projective arrangement

Publications mathematiques de l'IHES 101 (2005), 69-161.

Gert Heckman and Eduard Looijenga:
The moduli space of rational elliptic surfaces

Algebraic Geometry 2000, Azumino, Advanced Studies in Pure Mathematics 36 (2002), 185-248.

Gert Heckman:
Quantum integrability of the Kovalevsky top

Indag. Math. NS 9 (1998), 223-246.

Gert Heckman:
Dunkl Operators

Sem. Bourbaki 828, Asterisque 245 (1997), 223-246.

Gert Heckman and Eric Opdam:
Harmonic analysis for affine Hecke algebras

Current developments in Mathematics 1996, Intern. Press (1997), 37-60.

Gert Heckman and Eric Opdam:
Yang's system of particles and Hecke algebras

Ann. of Math. 145 (1997), 139-173.

Gert Heckman:
The volume of hyperbolic Coxeter polytopes of even dimension

Indag. Math. NS 6 (1995), 189-196.

Rogier Brussee, Gert Heckman and Eric Opdam:
Variation on a theme of Macdonald

Math. Z. 208 (1991), 1-10.

Gert Heckman:
An elementary approach to the hypergeometric shift operators of Opdam

Invent. Math. 103 (1991), 341-350.

Gert Heckman:
A remark on the Dunkl differential difference operators

Harmonic Analysis on Reductive Groups, Proceedings Bowdoin College 1989, Progr. Math. 101, Birkhauser (1991), 181-191.

Gert Heckman:
Hecke algebras and hypergeometric functions

Invent. Math. 100 (1990), 403-417.

F. Beukers and G. Heckman, Monodromy for the generalized hypergeometric function of Thomae, Invent. math. 95 (1989), 325-354.

Frits Beukers, W. Dale Brownawell and Gert Heckman, Siegel Normailty, Annals of Mathematics 127 (1988), 279-308.

G.J. Heckman, Root Systems and Hypergeometric Functions II, Compositio Mathematica 64 (1987), 353-373.

G.J. Heckman and E.M. Opdam, Root Systems and Hypergeometric Functions I, Compositio Mathematica 64 (1987), 329-352.

Michel Duflo, Gerrit Heckman et Michele Vergne, Projection d'orbites, formule de Kirillov et formule de Blattner, Mém. Soc. Math. France (N.S.) 15 (1984), 65-128.

J.J. Duistermaat and G.J. Heckman, Addendum to "On the Variation in the Cohomology of the Symplectic Form of the Reduced Phase Space", Invent. Math. 72 (1983), 153-158.

J.J. Duistermaat and G.J. Heckman, On the Variation in the Cohomology of the Symplectic Form of the Reduced Phase Space, Invent. Math. 69 (1982), 259-268.

G.J. Heckman, Projections of Orbits and Asymptotic Behavior of Multiplicities for Compact Connected Lie Groups, Invent. Math. 67 (1982), 333-356.

G.J. Heckman, Projections of Orbits and Asymptotic Behaviour of Multiplicities for Compact Lie Groups, Ph.D. University of Leiden, 1980


Education and Lecture Notes:

Gert Heckman:
Introduction to Riemannian Geometry, spring 2017

Gert Heckman:
Classical Differential Geometry, spring 2017

Gert Heckman:
On the Shoulders of Giants, spring 2017

Gert Heckman:
Coxeter Groups, fall 2016

Gert Heckman:
Hypergeometric Functions, fall 2015

Gert Heckman:
Symplectic Geometry, fall 2014

Gert Heckman:
Exercises Complex Functions, spring 2013

Gert Heckman:
Lie Algebras in Mathematics and Physics, fall 2009


Outreach (in Dutch):

Gert Heckman:
De Regenboog

Tekst Open Dag, November 2016

Gert Heckman:
In het paradijs van Cantor: spelen met oneindig

Tekst voordracht VWO-leerlingen, April 2016

Gert Heckman:
Escher en de wiskunde van betegelingen

Begeleidende tekst bij een voordracht voor Ars en Mathesis, 17 November 2012

Gert Heckman:
De Slinger van Foucault

Tekst voordracht VWO-leerlingen, Maart 2011

Maris van Haandel, Gert Heckman:
Kepler's wet over ellipsbanen onderwezen uit "Het Boek"

NTvN November 2007, 366-368


Miscellanea:

Gert Heckman:
Review of the book "Remembering Sofya Kovalevskaya" by M. Audin

Nieuw Archief Wiskunde, 2016

Gert Heckman:
In Memoriam Frans Clauwens

Nieuw Archief Wiskunde, 2012

Gert Heckman:
Hans Duistermaat and Henri Poincaré

Notices of the AMS, 2011

Gert Heckman:
Recollections of Hans Duistermaat

Nieuw Archief Wiskunde, 2010


PhD students:

Sander Rieken, Moduli of real curves of genus three, February 12, 2015: PhD Sander Rieken

Dali Shen, Hyperbolic structures on a toric arrangement complement February 4, 2015 (with Eduard Looijenga): PhD Dali Shen

Maarten van Pruijssen, Matrix Valued Orthogonal Polynomials related to Compact Gelfand Pairs of Rank One, December 19, 2012 (with Erik Koelink and Pablo Roman): PhD Maarten van Pruijssen

Peter Hochs, Quantisation Commutes with Reduction for Cocompact Hamiltonian Group Actions, February 8, 2008 (with Klaas Landsman): PhD Peter Hochs

Wim Couwenberg, Complex Reflections Groups and Hypergeometric Functions, November 21, 1994: PhD Wim Couwenberg

Eric Opdam, Generalized Hypergeometric Functions associated with Root Systems, January 29, 1988

Bert Ruitenburg, Invariant Ideals of Multiplicity Free Algebraic Group Actions, January 13, 1988


Master theses:

Hester Pieters:
Hyperbolic Reflection Groups and the Leech Lattice

Master thesis Hester Pieters, June 2011

Tim de Laat:
Regularization and Quantization of the Kepler Problem

Master thesis Tim de Laat, August 2010

Joris Mooij:
The vibrational spectrum of Buckminsterfullerene

Master thesis Joris Mooij, August 2003


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Last modified: August 26, 2013