Gorō Shimura | |
|---|---|
 Goro Shimura in 1964, taken byPrinceton University while he was a professor there | |
| Born | (1930-02-23)23 February 1930 |
| Died | 3 May 2019(2019-05-03) (aged 89) |
| Nationality | Japanese |
| Alma mater | University of Tokyo |
| Known for | Complex multiplication of abelian varieties Eichler-Shimura relation Modularity theorem Shimura correspondence Shimura variety Shimura subgroup Shimura's reciprocity law |
| Awards | Guggenheim Fellowship(1970) Cole Prize(1977) Asahi Prize(1991) Steele Prize(1996) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Princeton University |
| Doctoral students | Don Blasius Bill Casselman Melvin Hochster Robert Rumely Alice Silverberg |
Gorō Shimura (志村 五郎,Shimura Gorō, 23 February 1930 – 3 May 2019) was a Japanesemathematician and Michael Henry StraterProfessor Emeritus ofMathematics atPrinceton University who worked innumber theory,automorphic forms, andarithmetic geometry.[1] He was known for developing the theory ofcomplex multiplication of abelian varieties andShimura varieties, as well as posing theTaniyama–Shimura conjecture which ultimately led to theproof ofFermat's Last Theorem.
Gorō Shimura was born inHamamatsu,Japan, on 23 February 1930.[2] Shimura graduated with a B.A. in mathematics and a D.Sc. in mathematics from theUniversity of Tokyo in 1952 and 1958, respectively.[3][2]
After graduating, Shimura became a lecturer at the University of Tokyo, then worked abroad — including ten months in Paris and a seven-month stint at Princeton'sInstitute for Advanced Study — before returning to Tokyo, where he married Chikako Ishiguro.[4][2] He then moved from Tokyo to join the faculty ofOsaka University, but growing unhappy with his funding situation, he decided to seek employment in the United States.[4][2] ThroughAndré Weil he obtained a position at Princeton University.[4] Shimura joined the Princeton faculty in 1964 and retired in 1999, during which time he advised over 28 doctoral students and received theGuggenheim Fellowship in 1970, theCole Prize for number theory in 1977, theAsahi Prize in 1991, and theSteele Prize for lifetime achievement in 1996.[1][5]
Shimura described his approach to mathematics as "phenomenological": his interest was in finding new types of interesting behavior in the theory of automorphic forms. He also argued for a "romantic" approach, something he found lacking in the younger generation of mathematicians.[6] Shimura used a two-part process for research, using one desk in his home dedicated to working on new research in the mornings and a second desk for perfecting papers in the afternoon.[2]
Shimura had two children, Tomoko and Haru, with his wife Chikako.[2] Shimura died on 3 May 2019 inPrinceton,New Jersey at the age of 89.[1][2]
Shimura was a colleague and a friend ofYutaka Taniyama, with whom he wrote the first book on thecomplex multiplication of abelian varieties and formulated the Taniyama–Shimura conjecture.[7] Shimura then wrote a long series of major papers, extending the phenomena found in the theory ofcomplex multiplication of elliptic curves and the theory ofmodular forms to higher dimensions (e.g. Shimura varieties). This work provided examples for which the equivalence betweenmotivic andautomorphicL-functions postulated in theLanglands program could be tested:automorphic forms realized in thecohomology of a Shimura variety have a construction that attachesGalois representations to them.[8]
In 1958, Shimura generalized the initial work ofMartin Eichler on theEichler–Shimura congruence relation between thelocalL-function of amodular curve and the eigenvalues ofHecke operators.[9][10] In 1959, Shimura extended the work of Eichler on theEichler–Shimura isomorphism between Eichler cohomology groups and spaces ofcusp forms which would be used inPierre Deligne's proof of theWeil conjectures.[11][12]
In 1971, Shimura's work on explicitclass field theory in the spirit ofKronecker's Jugendtraum resulted in his proof ofShimura's reciprocity law.[13] In 1973, Shimura established theShimura correspondence between modular forms of half integral weightk+1/2, and modular forms of even weight 2k.[14]
Shimura's formulation of the Taniyama–Shimura conjecture (later known as the modularity theorem) in the 1950s played a key role in the proof of Fermat's Last Theorem byAndrew Wiles in 1995. In 1990,Kenneth Ribet provedRibet's theorem which demonstrated that Fermat's Last Theorem followed from the semistable case of this conjecture.[15] Shimura dryly commented that his first reaction on hearing ofAndrew Wiles's proof of the semistable case was 'I told you so'.[16]
His hobbies wereshogi problems of extreme length and collectingImari porcelain.The Story of Imari: The Symbols and Mysteries of Antique Japanese Porcelain is a non-fiction work about the Imari porcelain that he collected over 30 years that was published byTen Speed Press in 2008.[2][17]
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