Henk Broer Gert Heckman [de] Michael Ruzhansky [de; fr]
Biographyedit
Duistermaat attended primary school in Jakarta, at the time capital of the Dutch East Indies, where his family moved after the end of World War II. In 1957, a few years after the Indonesian independence, they came back to the Netherlands and Duistermaat completed his high school studies in Vlaardingen.[3][4]
From 1959 to 1965 he studied mathematics at Utrecht University, and he obtained his PhD degree at the same institution in 1968, with a thesis on the mathematical structures of thermodynamics entitled "Energy and Entropy as Real Morphisms for Addition and Order".[5] His original supervisor was the applied mathematician Günther K. Braun, who passed away one year before the thesis defense, so the official supervision was taken over by geometer Hans Freudenthal.[6][7][8][9]
After a postdoctoral stay in Lund (1969–70), Duistermaat returned to the Netherlands in 1971 and became in 1972 full professor in Nijmegen. In 1974 he returned to Utrecht, where he was offered the chair of Freudenthal.
Apart from being an eminent mathematician, Duistermaat 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.[4][7][16]
Duistermaat dropped thermodynamics after his PhD, due to dissents between mathematicians and physicists in Utrecht. Nevertheless, during his PhD research he read the work by Sophus Lie, and in particular encountered contact transformations. These topics exerted an important influence for his future pioneering works in microlocal analysis,[6][8][10] most prominently during his collaboration with Lars Hörmander, when they developed the theory of Fourier integral operators and proved the Propagation of singularities theorem [de].[17] This led him also to the work with Victor Guillemin on the link between spectra of elliptic operators and periodic bicharacteristics.[18]
His work with Alberto Grünbaum on the bispectral problem[28] was influential for integrable systems and noncommutative algebraic geometry.[7] In the last stages of his life he became interested in algebraic geometry[8][15] and wrote a book on QRT maps and elliptic surfaces.[29]
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 Spinc dirac operator, Boston: Birkhäuser, ISBN 978-0-8176-8247-7; Duistermaat, J. J. (1996). 1st edition. ISBN 0-8176-3865-2.[34]
Duistermaat, J. J.; Guillemin, V. W. (1975), "The spectrum of positive elliptic operators and periodic bicharacteristics" (PDF), Inventiones Mathematicae, 29 (1): 39–79, Bibcode:1975InMat..29...39D, doi:10.1007/BF01405172, hdl:10338.dmlcz/126178, MR 0405514, S2CID 189832135
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, Bibcode:1982InMat..69..259D, doi:10.1007/BF01399506, MR 0674406, S2CID 119943006
Duistermaat, J. J.; Grünbaum, F. A. (1986), "Differential equations in the spectral parameter", Communications in Mathematical Physics, 103 (2): 177–240, Bibcode:1986CMaPh.103..177D, doi:10.1007/bf01206937, MR 0826863, S2CID 121915958
Referencesedit
^"Hans Duistermaat". Geometry and Quantum Theory (GQT). Retrieved 2022-08-18.
^"In memoriam: Prof. dr. Johannes Jisse Duistermaat". Academia Europaea. Retrieved 2022-08-16.
^de Waard, Peter (2010-04-12). "De man van de formule" [The man of the formula]. De Volkskrant (in Dutch).
^ abcKreulen, Edwin (2010-04-19). "De wiskunde bleef altijd roepen. Hans Duistermaat 1942-2010" [Mathematics always keeps calling. Hans Duistermaat 1942-2010] (PDF). Trouw (in Dutch). p. 25.
^ abcdevan den Ban, Erik; Kolk, Johan (2010). "In Memoriam Hans Duistermaat (1942-2010): Grasping the essence" (PDF). Nieuw Archief voor Wiskunde. 11 (5): 235–237.
^ abcCushman, Richard (2011). "Hans Duistermaat (1942-2010)" (PDF). Newsletter of the European Mathematical Society. 79. European Mathematical Society: 17–19.
^ abcvan der Vorst, H.A. (2011). "Levensbericht Johannes Jisse Duistermaat" [Life story of Johannes Jisse Duistermaat] (PDF). Jaarboek - Koninklijke Nederlandse Akademie van Wetenschappen. Royal Netherlands Academy of Arts and Sciences.
^"Overlijden Hans Duistermaat" [Death of Hans Duistermaat]. Utrecht University (in Dutch). Retrieved 2022-08-16.
^"Lintjesregen: De opvallendste feiten op een rij" [Annual award celebration: the most notable facts in a row]. RTV Utrecht (in Dutch). 2007-04-27.
^ abcVũ Ngọc, San (2011). "Johannes Jisse (dit Hans) Duistermaat (1942-2010)" (PDF). La Gazette des mathématiciens (in French). 127. Société mathématique de France: 84–91.
^Beekman, Robert (2016). "Simultaan Karpov (1977)" [Simultaneous Karpov (1977)]. Schaakclub Oud Zuylen Utrecht (in Dutch). Retrieved 2022-08-16.
^Duistermaat, J. J.; Hörmander, L. (1972). "Fourier integral operators. II". Acta Mathematica. 128 (none): 183–269. doi:10.1007/BF02392165. ISSN 0001-5962. S2CID 189785151.
^Duistermaat, J. J.; Guillemin, V. W. (1975-02-01). "The spectrum of positive elliptic operators and periodic bicharacteristics". Inventiones Mathematicae. 29 (1): 39–79. Bibcode:1975InMat..29...39D. doi:10.1007/BF01405172. ISSN 1432-1297. S2CID 189832135.
^Duistermaat, J. J. (1980). "On global action-angle coordinates". Communications on Pure and Applied Mathematics. 33 (6): 687–706. doi:10.1002/cpa.3160330602.
^Cushman, R.; Duistermaat, J. J. (1988). "The quantum mechanical spherical pendulum". Bulletin of the American Mathematical Society. 19 (2): 475–479. doi:10.1090/S0273-0979-1988-15705-9. ISSN 0273-0979.
^Duistermaat, J. J.; Heckman, G. J. (1982-06-01). "On the variation in the cohomology of the symplectic form of the reduced phase space". Inventiones Mathematicae. 69 (2): 259–268. Bibcode:1982InMat..69..259D. doi:10.1007/BF01399506. ISSN 1432-1297. S2CID 119943006.
^Heckman, Gert (2010). "In Memoriam Hans Duistermaat (1942-2010): Recollections of a godsend talent" (PDF). Nieuw Archief voor Wiskunde. 11 (5): 240–241.
^Berline, Nicole; Vergne, Michèle (1982). "Classes caracteristiques equivariantes. Formule de localisation en cohomologie equivariante" [Equivariant characteristic classes. Localisation formula in equivariant cohomology]. Comptes rendus de l'Académie des sciences (in French). 295: 539–541.
^Atiyah, M.F.; Bott, R. (1984). "The moment map and equivariant cohomology". Topology. 23 (1): 1–28. doi:10.1016/0040-9383(84)90021-1.
^Duistermaat, J. J (1976-08-01). "On the Morse index in variational calculus". Advances in Mathematics. 21 (2): 173–195. doi:10.1016/0001-8708(76)90074-8. ISSN 0001-8708.
^Duistermaat, Hans; Guillemin, Victor; Meinrenken, Eckhard; Wu, Siye (1995). "Symplectic reduction and Riemann-Roch for circle actions". Mathematical Research Letters. 2 (3): 259–266. doi:10.4310/MRL.1995.v2.n3.a3.
^J. J., Duistermaat; Kolk, J. A. C. (2000). Lie Groups. Springer Verlag. doi:10.1007/978-3-642-56936-4. ISBN 978-3-540-15293-4.
^Duistermaat, J. J.; Grünbaum, F. A. (1986-06-01). "Differential equations in the spectral parameter". Communications in Mathematical Physics. 103 (2): 177–240. Bibcode:1986CMaPh.103..177D. doi:10.1007/BF01206937. ISSN 1432-0916. S2CID 121915958.
^Duistermaat, J. J. (2010). Discrete integrable systems : QRT Maps and Elliptic Surfaces. New York: Springer. ISBN 978-0-387-72923-7. OCLC 676697713.
^Stolk, Christiaan (2000). On the Modeling and Inversion of Seismic Data(PDF) (PhD thesis). Utrecht: Universiteit Utrecht. ISBN 90-393-2551-0.
^Duistermaat, Hans (2001). "The universal barrier function of a convex polytope". Circumspice. Various Papers in Around Mathematics in Honour of Arnoud van Rooij. Katholieke Universiteit Nijmegen: 207–220.
^Loog, Marco; Duistermaat, Johannes; Florack, Luc M. J. (2001). Kerckhove, Michael (ed.). "On the Behavior of Spatial Critical Points under Gaussian Blurring A Folklore Theorem and Scale-Space Constraints". Scale-Space and Morphology in Computer Vision. Berlin, Heidelberg: Springer: 183–192. doi:10.1007/3-540-47778-0_15. ISBN 978-3-540-47778-5.
^Hoyng, P.; Duistermaat, J. J. (2004-10-01). "Geomagnetic reversals and the stochastic exit problem". Europhysics Letters. 68 (2): 177. Bibcode:2004EL.....68..177H. doi:10.1209/epl/i2004-10243-1. ISSN 0295-5075. S2CID 250865891.
^Freed, Daniel S. (1997). "Review: The heat kernel Lefschetz fixed point formula for the Spinc dirac operator, by J. J. Duistermaat" (PDF). Bull. Amer. Math. Soc. (N.S.). 34 (1): 73–78. doi:10.1090/s0273-0979-97-00698-8.