# Hans Duistermaat

**Johannes Jisse (Hans) Duistermaat** (The Hague, December 20, 1942 – Utrecht, March 19, 2010) was a Dutch mathematician.
He studied mathematics at Utrecht University from 1959 to 1965 and obtained his PhD degree there in 1968 under the supervision of Hans Freudenthal. After a postdoctoral year 1969–70 in Lund, where he learned Fourier integral operators from Lars Hörmander, he went in 1971–74 to Nijmegen, where he became full professor in 1972. In 1974 he returned to Utrecht on the chair of professor Freudenthal, where he stayed until his unexpected death in March 2010.

Hans Duistermaat | |
---|---|

Born | |

Died | March 19, 2010 67) | (aged

Nationality | |

Alma mater | University of Utrecht |

Known for | Duistermaat–Heckman formula |

Scientific career | |

Fields | Mathematics |

Institutions | University of Utrecht |

Doctoral advisor | Hans Freudenthal |

Doctoral students | Reyer Sjamaar |

He became a member of the Royal Netherlands Academy of Arts and Sciences in 1982,[1] and Academy Professor in 2004. He supervised 25 PhD students.[2]

Duistermaat worked in many different areas of mathematics: classical mechanics, symplectic geometry, Fourier integral operators, partial differential equations, algebraic geometry, harmonic analysis, and dynamical systems. Apart from roughly 50 articles in refereed international journals, he has (co-)written 11 books. Among his best known research are his article with Victor Guillemin on spectra of elliptic operators and periodic bicharacteristics, his article with Gert Heckman on the Duistermaat–Heckman formula, and his article with Alberto Grünbaum on the bispectral problem.

Apart from being an eminent mathematician, he was also a good chess player. In a simultaneous match of 10 against Anatoly Karpov in 1977, Duistermaat was the only one who did not lose.

## Selected works

- Duistermaat, J. J. (2011) [1996],
*Fourier integral operators*, Modern Birkhäuser Classics, Birkhäuser/Springer, New York, doi:10.1007/978-0-8176-8108-1, ISBN 978-0-8176-8107-4, MR 1362544 - Duistermaat, J. J. (2011),
*The heat kernel Lefschetz fixed point formula for the Spin*, Boston: Birkhäuser, ISBN 978-0-8176-8247-7;^{c}dirac operator*1st edition*. 1996. ISBN 0-8176-3865-2.[3] - Duistermaat, J. J.; Guillemin, V. W. (1975), "The spectrum of positive elliptic operators and periodic bicharacteristics" (PDF),
*Inventiones Mathematicae*,**29**(1): 39–79, doi:10.1007/BF01405172, hdl:10338.dmlcz/126178, MR 0405514 - Duistermaat, J. J.; Heckman, G. J. (1982), "On the variation in the cohomology of the symplectic form of the reduced phase space",
*Inventiones Mathematicae*,**69**(2): 259–268, doi:10.1007/BF01399506, MR 0674406 - Duistermaat, J. J.; Grünbaum, F. A. (1986), "Differential equations in the spectral parameter",
*Communications in Mathematical Physics*,**103**(2): 177–240, doi:10.1007/bf01206937, MR 0826863

## References

- "J.J. Duistermaat (1942 - 2010)" (in Dutch). Royal Netherlands Academy of Arts and Sciences. Retrieved 14 July 2015.
- Johannes Jisse Duistermaat at the Mathematics Genealogy Project
- Freed, Daniel S. (1997). "Review:
*The heat kernel Lefschetz fixed point formula for the Spin*, by J. J. Duistermaat" (PDF).^{c}dirac operator*Bull. Amer. Math. Soc. (N.S.)*.**34**(1): 73–78. doi:10.1090/s0273-0979-97-00698-8.

- Ban, Erik van den; Kolk, Johan (2010), "Grasping the essence. In Memoriam Hans Duistermaat (1942–2010)" (PDF),
*Nieuw Archief voor Wiskunde*,**5/11**(4): 235–237, archived from the original (PDF) on 2011-09-29 - Guillemin, Victor; Pelayo, Álvaro; Ngoc, San Vu; et al., eds. (2011), "Remembering Johannes J. Duistermaat (1942--2010)",
*Notices of the American Mathematical Society*,**58**(6): 794–802, ISSN 0002-9920 - Vũ Ngọc, San (2011), "Johannes Jisse (dit Hans) Duistermaat (1942–2010)" (PDF),
*Gazette des Mathématiciens*(127): 84–91, ISSN 0224-8999, MR 2791390