Jürgen K. Moser | |
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| Born | (1928-07-04)July 4, 1928 |
| Died | December 17, 1999(1999-12-17) (aged 71) Schwerzenbach, Kanton Zürich, Switzerland |
| Alma mater | University of Göttingen |
| Known for | Moser stability theorem Moser's trick Moser–Neumann question Moser–Trudinger inequality De Giorgi–Nash–Moser theory Nash-Moser theorem Kolmogorov–Arnold–Moser theorem Harnack inequality Normalized solution Volterra lattice |
| Awards | ICM Speaker (1962, 1978, 1998) George David Birkhoff Prize (1968) James Craig Watson Medal (1969) Guggenheim Fellowship (1970) Gibbs Lecture (1973) Brouwer Medal (1984) John von Neumann Prize (1984) Cantor Medal (1992) Wolf Prize (1994/1995) |
| Scientific career | |
| Fields | Mathematics,mathematical analysis,dynamical systems,celestial mechanics,partial differential equations,complex analysis |
| Institutions | New York University,MIT,ETH Zürich |
| Doctoral advisor | Franz Rellich Carl Ludwig Siegel |
| Doctoral students | Charles Conley Håkan Eliasson |
| Other notable students | Paul Rabinowitz |
Jürgen Kurt Moser (July 4, 1928 – December 17, 1999) was a German-Americanmathematician, honored for work spanning over four decades, includingHamiltonian dynamical systems andpartial differential equations.
Moser's mother Ilse Strehlke was aniece of the violinist and composerLouis Spohr. His father was the neurologist Kurt E. Moser (July 21, 1895 – June 25, 1982), who was born to the merchant Max Maync (1870–1911) and Clara Moser (1860–1934). The latter descended from 17th century FrenchHuguenot immigrants toPrussia. Jürgen Moser's parents lived inKönigsberg,German empire and resettled inStralsund,East Germany as a result of theSecond World War. Moser attended theWilhelmsgymnasium (Königsberg) in his hometown, a high school specializing in mathematics and natural sciences education, from whichDavid Hilbert had graduated in 1880. His older brother Friedrich Robert Ernst (Friedel) Moser (August 31, 1925 – January 14, 1945) served in theGerman Army and died inSchloßberg during theEast Prussian offensive.
Moser married the biologist Dr. Gertrude C. Courant (Richard Courant's daughter,Carl Runge's granddaughter and great-granddaughter ofEmil DuBois-Reymond) on September 10, 1955 and took up permanent residence inNew Rochelle,New York in 1960, commuting to work inNew York City. In 1980 he moved to Switzerland, where he lived inSchwerzenbach nearZürich. He was a member of the Akademisches Orchester Zürich. He was survived by his younger brother, the photographic printer and processor Klaus T. Moser-Maync fromNorthport, New York, his wife, Gertrude Moser fromSeattle, their daughters, the theater designer Nina Moser from Seattle and the mathematician Lucy I. Moser-Jauslin fromDijon, and his stepson, the lawyer Richard D. Emery fromNew York City. Moser played thepiano and thecello, performingchamber music since his childhood in the tradition of a musical family, where his father played theviolin and his mother the piano. He was a lifelongamateur astronomer and took upparagliding in 1988 during a visit atIMPA inRio de Janeiro.
Moser completed his undergraduate education at and received hisDr. rer. nat. from theUniversity of Göttingen in 1952, studying underFranz Rellich. After his thesis, he came under the influence ofCarl Ludwig Siegel, with whom he coauthored the second and considerably expanded English language edition of a monography oncelestial mechanics. Having spent the year 1953 at theCourant Institute ofNew York University as aFulbright scholar, he emigrated to the United States in 1955 becoming a citizen in 1959.[1] He became a professor atMIT and later atNew York University. He served as director of theCourant Institute ofNew York University in the period of 1967–1970. In 1970 he declined the offer of a chair at theInstitute for Advanced Study inPrinceton. After 1980 he was atETH Zürich, becomingprofessor emeritus in 1995. He was director (sharing office withArmand Borel in the first two years) of the Forschungsinstitut für Mathematik at ETH Zürich in 1984–1995, where he succeededBeno Eckmann. He led a rebuilding of the ETH Zürich mathematics faculty. Moser was president of theInternational Mathematical Union in 1983–1986.
In 1967,Neil Trudinger identified a new function space embedding which could be viewed as a borderline case of theSobolev embedding theorem.[2] Moser found the sharp constant in Trudinger's inequality, with the corresponding result often known as theMoser–Trudinger inequality.[3]
In the late 1950s,Ennio De Giorgi andJohn Nash independently discovered the fundamentalelliptic regularity theory for general second-orderelliptic andparabolic partial differential equations, in which (unlike theSchauder estimates) no differentiability or continuity is assumed of the coefficients. In the 1960s, Moser identified a new approach to their basic regularity theory, introducing the technique ofMoser iteration. He developed it for both elliptic and parabolic problems, and beyond recovering De Giorgi and Nash's results, he was able to use it to prove a newHarnack inequality.[2][4] In his original work, a key role was played by an extension of theJohn–Nirenberg lemma.Enrico Bombieri later found an argument avoiding this lemma in the elliptic case, which Moser was able to adapt to the parabolic case. The collection of these regularity results are often known as De Giorgi–Nash–Moser theory, although the original results were due solely to De Giorgi and Nash.
In 1965, Moser found new results showing that any twovolume forms on aclosed manifold are related to one another by scaling and pullback by adiffeomorphism, so that geometrically the total volume is the only invariant of a volume form.[5] He was able to apply the same techniques tosymplectic forms, thereby proving that acohomologous family of symplectic forms are related to one another by diffeomorphisms: this is also known asMoser's stability theorem.[6] Moser also analyzed the case of manifolds with boundary, although his argument was mistaken. Later, withBernard Dacorogna, Moser fully carried out the analysis of the boundary case.
Moser also made an early contribution to theprescribed scalar curvature problem, showing that in anyconformal class ofRiemannian metrics on theprojective plane, every function except for those which are nonpositive arises as ascalar curvature.[7] Moser's prior analysis of the Moser–Trudinger inequality was important for this work, highlighting the geometric significance of optimal constants in functional inequalities.
Research ofHenri Poincaré andÉlie Cartan in the early twentieth century had clarified the two-dimensionalCR geometry, dealing with three-dimensionalhypersurfaces of smooth four-dimensional manifolds which are also equipped with acomplex structure. They had identified local invariants distinguishing two such structures, analogous to prior work identifying theRiemann curvature tensor and its covariant derivatives as fundamental invariants of a Riemannian metric. WithShiing-Shen Chern, Moser extended Poincaré and Cartan's work to arbitrary dimensions. Their work has had a significant influence on CR geometry.[8][9]
Among Moser's students were Mark Adler ofBrandeis University,Ed Belbruno,Charles Conley (1933–1984), Howard Jacobowitz ofRutgers University, andPaul Rabinowitz ofUniversity of Wisconsin.
Moser won the firstGeorge David Birkhoff Prize in 1968 for contributions to the theory ofHamiltonian dynamical systems, theJames Craig Watson Medal in 1969 for his contributions to dynamicalastronomy, theBrouwer Medal of theRoyal Dutch Mathematical Society in 1984, the Cantor Medal of theDeutsche Mathematiker-Vereinigung in 1992 and theWolf Prize in 1995 for his work on stability in Hamiltonian systems and on nonlinear differential equations. He was elected to membership of theNational Academy of Sciences in 1973 and was corresponding member of numerous foreign academies such as theLondon Mathematical Society and the Akademie der Wissenschaften und Literatur,Mainz. At three occasions he was an invited speaker at the quadrennialInternational Congress of Mathematicians, namely inStockholm (1962) in the section onapplied mathematics, inHelsinki (1978) in the section onComplex Analysis,[10] and a plenary speaker inBerlin (1998).[11] In 1990 he was awardedhonorary doctorates fromUniversity of Bochum and fromPierre and Marie Curie University inParis. TheSociety for Industrial and Applied Mathematics established a lecture prize in his honor in 2000.
Articles
Books
Name: Jurgen Kurt Moser; Age: 31; Birth Date: 4 Jul 1928; Issue Date: 2 Feb 1959; State: Massachusetts; Locality, Court: District of Massachusetts, District Court(subscription required)
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